Index to 2D 5-Neighbor Cellular Automata

Index to 2D 5-Neighbor Outer Totalistic Cellular Automata

Sequences in the OEIS related to 2D 5-Neighbor Outer Totalistic Cellular Automata are tabulated here.

Introduction

There are 2^32 possible rules for general two-dimensional Cellular Automata. Totalistic rules depend only upon the total number of ON cells in a neighborhood. Outer Totalistic rules also include the state of the center cell. The 5-Neighbor Outer Totalistic rules include the center cell and those to the N, E, S and W of it. 9-Neighbor rules would also consider neighbors that are diagonal to the center cell.

There are 1024 possible 2D 5-Neighbor Outer Totalistic Cellular Automata. Wolfram's numbering scheme identifies these by rule numbers from 0 to 1023. See "A New Kind of Science" by Stephen Wolfram, pages 170-179 or the Eric Weisstein's "World of Mathematics" links below. The sequences in the OEIS generally represent a two-dimensional cellular automata (CA) on a square grid representing successive generations or stages. This grid is initialized by a single black (ON) cell. Some rules will generate ON cells that nearly fill any grid size at stage 1. See rule 777 for example. So, in order to ensure finite values in these sequences, the grid is restricted to grow at only one cell in each direction at each stage. Thus, at stage n, the grid under consideration is 2n+1 cells on each side. Due to the definition of the rules and being initiated by a single cell, all resulting diagrams are symmetric along each axis and along each diagonal.

An example. The base 2 digits of the rule number determines the CA evolution. The last bit specifies the state of a cell if all neighbors are OFF and it too is OFF. The next to last bit specifies the state of a cell if all neighbors are OFF but the cell itself is ON. Then each earlier pair of bits specifies what should happen if progressively (Totalistic) more neighbors are black. So, bits 2^0 and 2^1 apply if none of the four neighbors are ON, bits 2^2 and 2^3 apply if one neighbor is ON, bits 2^4 and 2^5 apply if two neighbors are ON, bits 2^6 and 2^7 apply if three neighbors are ON and bits 2^8 and 2^9 apply if all four neighbors are ON. For example, Rule 614 equates to the bits {1,0,0,1,1,0,0,1,1,0}. Since we are considering 5-Neighbor Outer Totalistic CA the future state of a cell is determined by the four nearest neighbors (N,E,S,W) and the cell itself. Progressing from stage 0 to stage 1 we have to determine the new state of nine cells. The first cell (upper left corner) has the initial state of OFF and all neighbors are OFF, so bit 2^0 applies dictating that the new state is OFF. The second cell (middle of top row) has the initial state of OFF and one of its neighbors (the original ON cell from stage 0) is ON. One neighbor is ON so bits 2^2 and 2^3 apply. Since the initial state is OFF, bit 2^2 applies dictating that the new state is ON. Now skipping to the cell at the origin, no neighbors are ON and the initial state is ON, so bit 2^1 applies to dictate that the new state is ON. For rule 614, a more specific statement of the rule can be stated. The state of the cell is turned ON or remains ON only if an odd number of these five cells are ON. The first five stages (0-4) of the CA generated by Rule 614 are:

       Stage 0             Stage 1             Stage 2            Stage 3            Stage 4
                                                                                . . . . x . . . .
                                                               . . . x . . .    . . . . . . . . .
                                              . . x . .        . . x x x . .    . . . . . . . . .
                            . x .             . . . . .        . x . . . x .    . . . . . . . . .
          x                 x x x             x . x . x        x x . x . x x    x . . . x . . . x
                            . x .             . . . . .        . x . . . x .    . . . . . . . . .
                                              . . x . .        . . x x x . .    . . . . . . . . .
                                                               . . . x . . .    . . . . . . . . .
                                                                                . . . . x . . . .
 

Certain attributes of these CA can be interpreted as integer sequences. These are tabulated in the tables below. Perhaps the simplest attribute is the total number of ON cells at each stage. For example, the sequence generated by Rule 614 begins: 1,5,5,17,5,25,17,61,5,25,25,85 (A072272). Another sequence are the terms above only at at stages 2^n-1. This is relevant in the analysis of sequences such as Rule 614. See Sloane reference, "On the number of ON Cells in Cellular Automata" link below. The sequence generated by Rule 614 for this attribute begins: 1,5,17,61,217,773,2753 (A007483). Another sequence is the first difference of the total number of ON cells at each stage. This is simply the number of ON cells added at each stage, which could be negative. The sequence generated by Rule 614 for this attribute begins: 4,0,12,-12,20,-8,44,-56,20 (A170878). Another sequence is the partial sum of the total number of ON cells at each stage. This represents the total number of ON cells through n stages. The sequence generated by Rule 614 for this attribute begins: 1,6,11,28,33,58,75,136,141 (A253908).

Certain CA definitions (or rules), while different, generate identical sequences based solely on the number of ON cells. For example, rules 675 and 899 have different diagram sequences but have identical number of ON cells at each stage. The table below consolidates these rules that generate identical number of ON cells at each stage for the first 50 terms. It is conjectured that the ON cells remain identical for all terms for these rules.

Often a well known sequence like A005408 (The Odd Integers) comes very close to the CA generated sequence. The first term, usually a zero, may be missing or substituted. Or an extra first term will be present. In these cases the well known sequence is used in the tables below and the sequence is indicated with an asterisk. For example, the partial sums sequence based on Rule 4 begins 1,5,9,25,29,45,61,125. The OEIS sequence A116520 begins 0,1,5,9,25,29,45,61,125. This is a close match and will be used in the table below for Rule 4.

Sequences in the OEIS Related to 2D 5-Neighbor Outer Totalistic Cellular Automata Describing the Total Number of ON Cells

Column headings in the table below:

Rule         Wolfram's Rule Number(s) 
Sequence     First seven terms of the number of ON cells sequence
ON           A-number of the sequence listing the number of ON cells at each stage of the CA evolution
ON(2^n-1)    A-number of the sequence listing the number of ON cells at stages 2^n-1, n=0,...
Partial Sum  A-number of the sequence listing the partial sums of the number of ON cells at each stage
First Diff   A-number of the sequence listing the first differences of the number of ON cells at each stage
             (an asterisk, "*", in an A-number indicates a near match)

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS

Rule	Sequence	ON	ON(2^n-1)	Partial Sum	First Diff
0,8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144, 152,160,168,176,184,192,200,208,216,224,232,240,248,256,264, 272,280,288,296,304,312,320,328,336,344,352,360,368,376,384, 392,400,408,416,424,432,440,448,456,464,472,480,488,496,504, 512,520,528,536,544,552,560,568,576,584,592,600,608,616,624, 632,640,648,656,664,672,680,688,696,704,712,720,728,736,744, 752,760,768,776,784,792,800,808,816,824,832,840,848,856,864, 872,880,888,896,904,912,920,928,936,944,952,960,968,976,984, 992,1000,1008,1016	1,0,0,0,0,0,0	A000007	A000007	A000012	A154955*
1,9,17,25,257,265,273,281	1,4,1,44,1,116,1	A269906	A269907	A269908	A269909
2,10,18,26,34,42,50,58,66,74,82,90,98,106,114,122,130,138,146, 154,162,170,178,186,194,202,210,218,226,234,242,250,258,266, 274,282,290,298,306,314,322,330,338,346,354,362,370,378,386, 394,402,410,418,426,434,442,450,458,466,474,482,490,498,506, 514,522,530,538,546,554,562,570,578,586,594,602,610,618,626, 634,642,650,658,666,674,682,690,698,706,714,722,730,738,746, 754,762,770,778,786,794,802,810,818,826,834,842,850,858,866, 874,882,890,898,906,914,922,930,938,946,954,962,970,978,986, 994,1002,1010,1018	1,1,1,1,1,1,1	A000012	A000012	A000027	A000004
3,11,19,27,67,75,83,91	1,5,1,45,1,117,1	A269910	A269911	A269912	A269913
4,12,36,44,68,76,100,108,132,140,164,172,196,204,228,236,516, 524,548,556,580,588,612,620,644,652,676,684,708,716,740,748	1,4,4,16,4,16,16	A102376	A000302	A116520*	A269880
5,13,21,29,37,45,53,61,69,77,85,93,101,109,117,125	1,8,0,49,0,121,0	A270006	A270007	A270008	A270009
6,38,70,102,134,166,198,230	1,5,4,20,4,20,16	A269695	A269696	A269697	A269698
7,15,23,31,39,47,55,63,71,79,87,95,103,111,119,127,135,143,151, 159,167,175,183,191,199,207,215,223,231,239,247,255,263,271, 279,287,295,303,311,319,327,335,343,351,359,367,375,383,391, 399,407,415,423,431,439,447,455,463,471,479,487,495,503,511	1,9,0,49,0,121,0	A270010	A270011	A270012	A270013
14,46,142,174	1,5,8,20,20,32,40	A269707	A269708	A269709	A269710
20,28,52,60,148,156,180,188,532,540,564,572,660,668,692,700	1,4,8,12,20,24,44	A269711	A269712	A269713	A269714
22	1,5,8,20,16,44,32	A269715	A269716	A269717	A269718
30	1,5,12,16,36,24,60	A269753	A269754	A269755	A269756
33	1,4,5,32,9,92,21	A269810	A269811	A269812	A269813
35	1,5,5,37,9,101,21	A269814	A269815	A269816	A269817
41	1,4,5,32,13,84,29	A269872	A269873	A269874	A269875
43,59	1,5,5,37,13,97,25	A269876	A269815	A269878	A269879
49	1,4,5,32,9,100,21	A270014	A270015	A270016	A270017
51	1,5,5,37,9,109,13	A270018	A270019	A270020	A270021
54	1,5,8,20,28,40,44	A270022	A270023	A270024	A270025
57	1,4,5,32,13,84,29	A270075	A270076	A270077	A270078
62	1,5,12,20,32,44,68	A270079	A270080	A270081	A270082
65,321	1,4,5,36,9,96,17	A269782	A270084	A270085	A270086
73	1,4,5,40,0,121,0	A270087	A270088	A270089	A270090
78	1,6,14,34,54,86,134	A270091	A270092	A270093	A270094
81	1,4,5,40,9,100,21	A270098	A270099	A270100	A270101
84,92,116,124,212,220,244,252,596,604,628,636,724,732,756,764	1,4,8,16,16,32,32	A189007	A000302	A270106	A270107
86	1,5,8,24,16,48,32	A270125	A270126	A270127	A270128
89	1,4,5,44,0,121,0	A270129	A270130	A270131	A270132
94	1,5,12,16,36,24,60	A270133	A270134	A270135	A270136
97	1,4,9,32,13,84,21	A270152	A270153	A270154	A270155
99	1,5,5,41,12,109,16	A270156	A270157	A270158	A270159
105	1,4,9,32,13,92,45	A270160	A270161	A270162	A270163
107	1,5,5,41,12,109,16	A270164	A270165	A270166	A270167
110	1,5,8,20,20,32,48	A270168	A270169	A270170	A270171
113	1,4,9,32,17,88,37	A270177	A270178	A270179	A270180
115	1,5,5,41,12,109,16	A270181	A270182	A270183	A270184
118	1,5,8,24,24,48,36	A270185	A270186	A270187	A270188
121	1,4,9,32,17,100,40	A270206	A270207	A270208	A270209
123	1,5,5,41,12,109,16	A270210	A270211	A270212	A270213
126	1,5,12,20,36,40,80	A270214	A173034	A270215	A270216
129,385	1,4,5,28,9,84,21	A270217	A270218	A270219	A270220
131	1,5,5,33,13,93,25	A270221	A270222	A270223	A270224
133	1,8,4,40,17,100,25	A270232	A270233	A270234	A270235
137	1,4,5,28,9,84,29	A270274	A270275	A270276	A270277
139	1,5,5,33,13,93,33	A270278	A270279	A270280	A270281
141	1,8,4,40,17,108,17	A270282	A270283	A270284	A270285
145,153	1,4,5,32,4,101,20	A270286	A270287	A270288	A270289
147	1,5,5,37,4,105,20	A270290	A270291	A270292	A270293
149	1,8,4,44,5,116,12	A270317	A270318	A270319	A270320
150	1,5,8,20,20,44,3	A270321	A270322	A270323	A270324
155	1,5,5,37,8,97,25	A270325	A270326	A270327	A270328
157	1,8,4,44,5,116,12	A270329	A270330	A270331	A270332
158	1,5,12,20,32,32,64	A270333	A270334	A270335	A270336
161	1,4,9,24,29,64,49	A270450	A270451	A270452	A270453
163,171,227,235	1,5,9,33,25,85,49	A270454	A270222	A270455	A270456
165	1,8,4,40,17,104,20	A270457	A270458	A270459	A270460
169	1,4,9,24,29,68,41	A270461	A270462	A270463	A270464
173	1,8,4,40,17,112,20	A270465	A270466	A270467	A270468
177	1,4,9,32,33,84,65	A270618	A270619	A270620	A270621
179	1,5,9,41,21,93,41	A270622	A270623	A270624	A270625
181	1,8,4,44,9,108,21	A270626	A270627	A270628	A270629
182	1,5,8,20,32,36,52	A270630	A270631	A270632	A270633
185	1,4,9,32,33,92,65	A270634	A270635	A270636	A270637
187	1,5,9,41,21,93,49	A270673	A270674	A270675	A270676
189	1,8,4,44,9,108,21	A270677	A270678	A270679	A270680
190,254	1,5,12,24,32,52,60	A270681	A270682	A270683	A270684
193	1,4,9,24,21,72,45	A270685	A270686	A270687	A270688
195	1,5,5,33,13,93,25	A270689	A270690	A270691	A270692
197	1,8,4,40,17,100,25	A270716	A270717	A270718	A270719
201	1,4,9,28,17,80,28	A270720	A270721	A270722	A270723
203	1,5,5,33,13,93,33	A270725	A270726	A270727	A270728
205	1,8,4,40,17,108,17	A270729	A270730	A270731	A270732
206	1,5,8,20,20,32,48	A270733	A270734	A270735	A270736
209	1,4,9,28,25,80,53	A270891	A270892	A270893	A270894
211	1,5,5,37,4,105,20	A270897	A270898	A270899	A270900
213	1,8,4,44,9,112,21	A270901	A270902	A270903	A270904
214	1,5,8,24,20,60,28	A270905	A270906	A270907	A270908
217	1,4,9,32,9,96,44	A270909	A270910	A270911	A270912
219	1,5,5,37,8,97,25	A270930	A270931	A270932	A270933
221	1,8,4,44,9,116,9	A270934	A270935	A270936	A270937
222	1,5,12,20,32,32,72	A270938	A270939	A270940	A270941
225	1,4,13,28,33,84,61	A270942	A270943	A270944	A270945
229	1,8,4,40,17,104,20	A270946	A270947	A270948	A270949
233	1,4,13,32,21,68,40	A270976	A270977	A270978	A270979
237	1,8,4,40,17,112,20	A270980	A270981	A270982	A270983
238	1,5,8,20,20,32,48	A270984	A270985	A270986	A270987
241	1,4,13,36,37,88,77	A270988	A270989	A270990	A270991
243	1,5,9,41,21,101,49	A269702	A271001	A271002	A271003
245	1,8,4,44,13,112,25	A271004	A271005	A271006	A271007
246	1,5,8,24,28,48,36	A271008	A271009	A271010	A271011
249	1,4,13,40,25,88,81	A271012	A271013	A271014	A271015

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)

Rule	Sequence	ON	ON(2^n-1)	Partial Sum	First Diff
251	1,5,9,41,21,101,49	A271016	A271017	A271018	A271019
253	1,8,4,44,13,116,13	A271051	A270935	A271052	A271053
259	1,5,5,36,5,108,5	A271054	A271055	A271056	A271057
260,268,292,300,388,396,420,428,772,780,804,812,900,908,932,940	1,4,5,12,4,16,20	A253086	A253087	A255150	A271059
261,269,277,285,293,301,309,317,325,333,341,349,357,365,373,381	1,8,1,48,1,120,1	A271060	A271061	A271062	A271064
262	1,5,4,20,9,33,13	A271065	A271066	A271067	A271068
267	1,5,5,40,13,100,13	A271083	A271084	A271085	A271086
270	1,5,8,21,20,28,36	A271087	A271088	A271089	A271090
275	1,5,5,40,5,112,5	A271091	A271092	A271093	A271094
276,284,308,316,340,348,372,380,404,412,436,444,468,476,500,508, 788,796,820,828,852,860,884,892,916,924,948,956,980,988,1012,1020	1,4,9,16,25,36,49	A000290*	A000302	A000330*	A005408*
278	1,5,8,20,16,44,32	A271095	A271096	A271097	A271098
283	1,5,5,44,5,109,16	A271117	A271118	A271119	A271120
286	1,5,12,17,37,28,76	A271121	A271122	A271123	A271124
289	1,4,5,32,9,92,21	A271125	A271126	A271127	A271128
291	1,5,9,32,9,101,41	A271129	A271130	A271131	A271132
294	1,5,4,20,9,33,17	A271133	A271136	A271134	A271135
297	1,4,5,32,13,88,17	A271148	A271149	A271150	A271151
299	1,5,9,32,9,101,45	A271152	A271153	A271154	A271155
302	1,5,8,21,24,37,44	A271156	A271157	A271158	A271159
305	1,4,5,32,9,100,21	A271160	A271161	A271162	A271163
307	1,5,9,32,13,104,25	A271164	A271165	A271166	A271167
310	1,5,8,20,28,40,45	A271195	A271196	A271198	A271199
313	1,4,5,32,13,88,21	A271200	A271201	A271202	A271203
315	1,5,9,32,13,104,25	A266206	A270565	A271248	A271249
318	1,5,12,21,37,40,68	A271250	A271251	A271252	A271253
323	1,5,5,36,9,96,17	A270565	A271254	A271255	A271256
324,332,356,364,452,460,484,492,836,844,868,876,964,972,996,1004	1,4,5,12,8,24,25	A246316	A246317	A271257	A271258
326	1,5,4,20,9,37,24	A271259	A271260	A271261	A271262
329	1,4,5,40,9,100,5	A265689	A271274	A271275	A271276
331	1,5,5,40,13,100,21	A271277	A271278	A271279	A271280
334	1,5,8,21,20,32,44	A271281	A271282	A271283	A271284
337	1,4,5,40,9,100,21	A271285	A271286	A271287	A271288
339	1,5,5,40,9,100,25	A271289	A271290	A271291	A271292
342	1,5,8,24,17,53,32,96	A264797	A270126	A269511	A269512
345	1,4,5,44,5,104,13	A271293	A271294	A271295	A271296
347	1,5,5,44,5,109,16	A271297	A271298	A271299	A271300
350	1,5,12,17,37,28,76	A271301	A271302	A271303	A271304
353	1,4,9,32,13,84,21	A271305	A271306	A271307	A271308
355	1,5,9,32,17,101,36	A271397	A271398	A271399	A271408
358	1,5,4,20,9,37,24	A271409	A271411	A271412	A271413
361	1,4,9,32,13,92,45	A271414	A271415	A271416	A271417
363	1,5,9,32,17,101,40	A264099	A268153	A268154	A268194
366	1,5,8,21,24,37,52	A268195	A268202	A268275	A268276
369	1,4,9,32,17,92,37	A268277	A268282	A268503	A270793
371	1,5,9,32,21,96,41	A271454	A271455	A271456	A271457
374	1,5,8,24,25,53,36	A169701	A271458	A271459	A271460
377	1,4,9,32,17,104,29	A271461	A271462	A271463	A271464
379	1,5,9,32,21,96,41	A265916	A270423	A271537	A271538
382	1,5,12,21,37,40,76	A271539	A271540	A271541	A271542
387	1,5,9,24,17,84,41	A271543	A271544	A271545	A271546
389	1,8,5,40,17,104,17	A271594	A271595	A271596	A271597
390	1,5,4,20,9,33,13	A271598	A271599	A271600	A271601
393	1,4,5,28,9,84,29	A271602	A271603	A271604	A271605
395	1,5,9,28,17,89,32	A271685	A271686	A271687	A271688
397	1,8,5,44,17,108,33	A271689	A271690	A271691	A271692
398	1,5,8,21,20,28,36	A271693	A271694	A271695	A271696
401,409	1,4,5,32,5,96,17	A271803	A271804	A271805	A271806
403	1,5,9,28,17,96,45	A271807	A271808	A271809	A271810
405	1,8,5,44,5,116,17	A271812	A271813	A271814	A271815
406	1,6,14,34,54,102,139	A271885	A271887	A271772	A271888
411	1,5,9,32,25,93,48	A271889	A271890	A271891	A271892
413,445,477,509	1,8,5,48,5,120,5	A272007	A271061	A272009	A272010
414	1,5,12,21,32,40,81	A272012	A272013	A272014	A272015
417	1,4,9,28,17,68,41	A272016	A272017	A272018	A272019
419	1,5,13,28,25,101,56	A272045	A272046	A272047	A272048
421	1,8,5,40,17,108,29	A272049	A272050	A272051	A272052
422	1,5,4,20,9,33,17	A272085	A272086	A272087	A272088
425	1,4,9,28,17,68,41	A272089	A272218	A272091	A272092
427	1,5,13,32,37,89,80	A271902	A271903	A271904	A272110
429	1,8,5,44,17,108,33	A272111	A272112	A272113	A272114
430	1,5,8,21,24,37,44	A272115	A002450*	A272116	A272117
433	1,4,9,36,25,88,65	A272145	A272146	A272147	A272148
435	1,5,13,36,33,92,65	A272149	A272150	A272151	A272152
437	1,8,5,44,9,112,21	A272153	A272154	A272155	A272156
438	1,5,8,20,32,40,36	A272217	A272218	A272219	A272220
441	1,4,9,36,25,96,65	A272221	A272222	A272223	A272224
443	1,5,13,40,25,97,72	A272225	A272226	A272227	A272228
446	1,5,12,25,28,52,64	A272194	A272249	A272250	A272251
449	1,4,9,24,21,72,45	A272252	A272253	A272254	A272255
451	1,5,9,24,21,72,45	A272256	A272257	A272258	A270844
453	1,8,5,40,17,104,29	A272273	A272274	A272275	A272276
454	1,5,4,20,9,37,28	A246326	A272277	A272278	A272279
457	1,4,9,28,21,92,57	A272280	A272281	A2722782	A272283
459	1,5,9,28,25,81,32	A272287	A272288	A272289	A272290
461	1,8,5,44,17,112,21	A272291	A272292	A272293	A272294
462	1,5,8,21,20,32,48	A246330	A272310	A272311	A272312
465	1,4,9,28,25,84,49	A272313	A272218	A272316	A272317
467	1,5,9,28,29,80,53	A272315	A272319	A272320	A272321
469	1,8,5,44,9,112,21	A272416	A272417	A272418	A272419
470	1,5,8,24,21,56,32	A253078	A272420	A272421	A272422
473	1,4,9,32,21,100,41	A272423	A272424	A272425	A272426
475	1,5,9,32,29,84,61	A272447	A272448	A272449	A272450
478	1,5,12,21,32,44,73	A272451	A272452	A272453	A272454
481	1,4,13,28,33,84,69	A272455	A272456	A272457	A272458
483	1,5,13,28,37,85,76	A248860	A267828	A267829	A272346
485	1,8,5,40,17,108,37	A272350	A272396	A272504	A272505
486	1,5,4,20,9,37,28	A272506	A272507	A272508	A272509
489	1,4,13,32,33,100,65	A272510	A272511	A272512	A272513

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)

Rule	Sequence	ON	ON(2^n-1)	Partial Sum	First Diff
491	1,5,13,32,41,76,77	A272539	A272540	A272541	A272542
493	1,8,5,44,17,112,29	A272543	A272544	A272545	A272546
494	1,5,8,21,24,37,52	A169705	A272547	A272548	A169706
497	1,4,13,36,37,88,85	A272556	A272557	A272558	A272559
499	1,5,13,36,37,88,85	A272560	A272561	A272562	A272563
501	1,8,5,44,13,112,25	A272564	A271005	A272566	A272567
502	1,5,8,24,29,48,56	A272577	A272578	A272579	A272580
505	1,4,13,40,29,100,69	A272581	A271286	A272583	A272584
507	1,5,13,40,29,100,69	A272585	A272586	A272587	A272588
510	1,5,12,25,28,56,56	A169699	A092440	A272700	A169700
513,769	1,4,13,24,53,65,113	A272702	A059153	A272703	A272704
515,523	1,5,13,25,49,69,109	A272705	A272706	A272707	A272708
517	1,8,20,37,60,84,129	A272730	A272731	A272732	A272733
518,550,582,614	1,5,5,17,5,25,17	A072272	A007483	A253908	A170878
519,527,535,543,551,559,567,575,583,591,599,607,615,623,631,639,647, 655,663,671,679,687,695,703,711,719,727,735,743,751,759,767,775,783, 791,799,807,815,823,831,839,847,855,863,871,879,887,895,903,911,919, 927,935,943,951,959,967,975,983,991,999,1007,1015,1023	1,9,25,49,81,121,169	A016754	A060867	A000447*	A008590*
521	1,4,13,24,53,69,105	A272734	A272735	A272736	A272737
525	1,8,20,37,60,84,129	A272738	A272739	A272740	A272741
526	1,5,9,17,17,33,45	A272742	A272743	A272744	A272745
529	1,4,13,28,49,77,96	A272746	A272747	A272748	A272749
531	1,5,13,29,49,89,97	A272750	A272751	A272752	A272753
533	1,8,20,37,64,84,141	A272782	A272783	A272784	A272785
534	1,5,9,21,17,49,29	A272786	A272787	A272788	A272789
537	1,4,13,28,49,81,88	A272790	A272791	A272792	A272793
539	1,5,13,29,49,89,105	A272801	A272802	A272803	A272804
541	1,8,20,37,64,84,141	A272805	A272806	A272807	A272808
542	1,5,13,21,33,37,69	A272809	A272810	A272811	A272812
545	1,4,17,28,57,84,117	A272834	A272835	A272836	A272837
547	1,5,17,29,61,89,121	A272838	A272839	A272840	A272841
549	1,8,20,41,60,97,132	A272842	A272843	A272844	A272845
553	1,4,17,28,57,84,125	A272846	A272218	A272848	A272849
555,571	1,5,17,29,61,89,129	A272920	A272921	A272922	A272923
557	1,8,20,41,60,97,132	A272924	A272925	A272926	A272927
558,686	1,5,9,21,25,37,49	A147562*	A002450*	A272928	A147582*
561	1,4,17,28,61,89,121	A272769	A272936	A272937	A272938
563	1,5,17,29,61,89,121	A272939	A272940	A272941	A272942
565	1,8,20,41,60,101,137	A272943	A272944	A272945	A272946
566	1,5,9,21,29,37,49	A272986	A272987	A272989	A272990
569	1,4,17,28,61,93,133	A272991	A272992	A272993	A272994
573	1,8,20,41,60,101,141	A272995	A272996	A272997	A272998
574,638,702,766,830,894,958,1022	1,5,13,25,41,61,85	A001844	A092440	A005900*	A008586*
577	1,4,17,25,52,73,113	A273022	A273023	A273024	A273025
579	1,5,13,29,57,73,121	A273026	A273027	A273028	A273029
581	1,8,20,41,57,96,116	A273069	A273070	A273071	A273072
585	1,4,17,29,49,81,133	A273073	A273074	A273075	A273076
587	1,5,13,29,57,73,121	A273077	A273078	A273079	A273080
589	1,8,20,41,61,93,129	A273111	A273112	A273113	A273114
590	1,5,9,17,17,37,49	A273115	A273116	A273117	A273118
593	1,4,17,25,60,65,137	A273119	A273120	A273121	A273122
595	1,5,13,33,49,93,97	A272161	A273141	A273142	A273143
597	1,8,20,41,57,104,116	A273144	A273145	A273146	A273147
598	1,5,9,21,17,53,41	A273150	A002450*	A273151	A273152
601	1,4,17,29,61,73,132	A272330	A272373	A272824	A272825
603	1,5,13,33,49,93,105	A272828	A272833	A273173	A273174
605	1,8,20,41,61,105,125	A273175	A273176	A273177	A273178
606	1,5,13,21,33,37,77	A273204	A273205	A273206	A273207
609	1,4,21,29,72,84,141	A273208	A273209	A273210	A273211
611	1,5,17,37,61,97,133	A273212	A273213	A273214	A273215
613	1,8,20,45,61,112,132	A273241	A273242	A273243	A273244
617	1,4,21,29,72,88,152	A273246	A273247	A273248	A273249
619,635	1,5,17,37,65,101,137	A273250	A273251	A273252	A273253
621	1,8,20,45,61,112,136	A273266	A273267	A273268	A273269
622	1,5,9,21,25,37,57	A269522	A269566	A269567	A269568
625	1,4,21,29,72,84,141	A273270	A273271	A273272	A273273
627	1,5,17,37,61,101,121	A273274	A273275	A273276	A273277
629	1,8,20,45,61,112,132	A273295	A273296	A273297	A273298
630	1,5,9,21,29,45,65	A269523	A267268	A269543	A269629
633	1,4,21,29,72,88,156	A273299	A273300	A273301	A273303
637	1,8,20,45,61,112,136	A273304	A273305	A273306	A273307
641,649,897,905	1,4,17,40,73,112,161	A273309	A273310	A273311	A273312
643,651,707,715	1,5,17,41,73,113,161	A166147*	A273313	A273314	A273315
645,653,661,669,677,685,693,701,709,717,725,733,741,749,757,765	1,8,24,48,80,120,168	A033996*	A271061	A273316	A008590*
646	1,5,5,17,9,29,17	A273326	A273327	A273328	A273329
654	1,5,9,17,21,29,37	A273330	A273331	A273332	A273333
657,665	1,4,17,48,80,120,168	A273334	A273335	A273336	A273337
659,667,723,731	1,5,17,49,81,121,169	A273384	A273385	A273386	A273387
662	1,5,9,21,21,45,33	A273388	A273389	A273390	A273391
670	1,5,13,21,33,49,61	A273392	A273393	A273394	A273395
673,681,689,697	1,4,21,44,77,116,165	A273405	A269907	A273406	A273407
675,683,691,699,739,747,755,763	1,5,21,45,77,117,165	A078371*	A269911	A273408	A234275*
678	1,5,5,17,9,29,21	A079317	A052539*	A273409	A151921
694	1,5,9,21,33,45,53	A273410	A272832	A273411	A273412
705,713	1,4,21,41,72,113,160	A273417	A273418	A273419	A273420
710	1,5,5,17,9,29,17	A273421	A273422	A273423	A273424
718	1,5,9,17,21,29,37	A273425	A273426	A273427	A273428
721,729	1,4,21,41,80,120,168	A273443	A273446	A273447	A273448
726	1,5,9,21,21,53,53	A273449	A273450	A273451	A273452
734	1,5,13,21,33,49,61	A273453	A273454	A273455	A273456
737,745,753,761,993,1001,1009,1017	1,4,25,49,81,121,169	A016754*	A060867*	A273480	A273481
742	1,5,5,17,9,29,21	A273482	A273483	A273484	A273485
750	1,5,9,21,25,37,57	A169707	A002450*	A253098	A169708
758	1,5,9,21,33,45,61	A273486	A273489	A273490	A273491
771,787,835,851	1,5,17,33,65,89,137	A273499	A272022	A273500	A273501
773,781,789,797,837,845,853,861	1,8,21,40,65,96,133	A000567*	A165665	A002414	A016921*
774	1,5,5,17,5,25,17	A273502	A273503	A273504	A273505
777	1,4,13,24,53,69,105	A273414	A273444	A273532	A273533
779,795,843,859	1,5,17,37,61,97,125	A273538	A273539	A273540	A273541
782	1,5,9,17,17,33,53	A273534	A273535	A273536	A273537
785	1,4,13,28,49,77,104	A273557	A273558	A273559	A273560
790,854	1,5,9,25,29,53,49	A273561	A092440	A273562	A273563
793	1,4,13,28,49,81,108	A273564	A273565	A273566	A273567

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (concluded)

Rule	Sequence	ON	ON(2^n-1)	Partial Sum	First Diff
798,862	1,5,13,21,37,41,85	A273569	A273570	A273571	A273572
801	1,4,17,28,57,84,117	A273573	A273574	A273575	A273576
803,811,819,827,867,875,883,891	1,5,21,33,77,105,153	A273577	A270222	A273578	A273579
805,821,869,885	1,8,21,44,69,113,145	A273602	A273603	A273604	A273605
806	1,5,5,17,5,25,17	A273606	A273607	A273608	A273609
809	1,4,17,28,57,84,125	A273610	A273611	A273612	A273613
813,829,877,893	1,8,21,44,69,117,153	A258448	A273639	A273640	A273641
814	1,5,9,21,29,41,53	A273642	A273643	A273644	A273645
817	1,4,17,28,61,89,121	A273646	A273647	A273648	A273649
822,886	1,5,9,25,37,49,57	A269918	A272762	A272847	A273370
825	1,4,17,28,61,93,141	A273430	A273431	A273581	A273674
833,849	1,4,17,33,56,85,120	A273675	A273676	A273677	A273678
838	1,5,5,17,5,25,17	A273544	A273680	A273681	A273682
841,857	1,4,17,37,61,97,124	A273683	A273684	A273685	A273686
846	1,5,9,17,17,37,53	A273687	A273688	A273689	A273690
865,881	1,4,21,33,68,105,140	A273699	A273700	A273701	A273702
870	1,5,5,17,5,25,17,61	A273703	A273704	A273705	A273706
873,889	1,4,21,33,68,105,144	A273707	A273708	A273709	A273710
878	1,5,9,21,29,41,61,65	A273739	A273740	A273741	A273742
899,907,915,923,963,971,979,987	1,5,21,45,77,117,165	A265056	A269911	A273408	A234275*
901,909,917,925,933,941,949,957,965,973,981,989,997,1005,1013,1021	1,8,25,49,81,121,169	A273743	A270007	A273744	A273745
902	1,5,5,17,9,29,17	A273758	A273759	A273760	A273761
910	1,5,9,17,21,29,37	A273762	A273763	A273764	A273765
913,921	1,4,17,48,81,121,169	A273766	A273767	A273768	A273769
918,982	1,5,9,25,29,53,53	A273746	A273747	A273748	A273749
926,990	1,5,13,21,37,45,77	A273750	A002450*	A273778	A273779
929,937,945,953	1,4,21,48,81,121,169	A273780	A273767	A273781	A273782
931,939,947,955,995,1003,1011,1019	1,5,25,49,81,121,169	A273789	A273385	A273790	A273791
934	1,5,5,17,9,29,21	A273792	A273793	A273794	A273795
942	1,5,9,21,29,41,53	A169649*	A273796	A273797	A169648*
950,1014	1,5,9,25,37,53,65	A273827	A273828	A273829	A273830
961,977	1,4,21,45,76,117,164	A273831	A273832	A273833	A273834
966	1,5,5,17,9,29,17	A273835	A273836	A273837	A273838
969,985	1,4,21,45,76,121,169	A273847	A273848	A273849	A273850
974	1,5,9,17,21,29,37	A273851	A273852	A273853	A273854
998	1,5,5,17,9,29,21	A273855	A273856	A273857	A273858
1006	1,5,9,21,29,41,61	A169709	A273860	A273861	A169710

Sequences in the OEIS Related to 2D 5-Neighbor Outer Totalistic Cellular Automata Related to the Position of ON Cells Along the X-Axis

Column headings in the table below:

Rule      Wolfram's Rule Number(s) 
Left(B)   Sequence describing the binary representation of the x-axis from the left edge to the origin
Right(B)  Sequence describing the binary representation of the x-axis from the origin to the right edge
Left(D)   Sequence describing the decimal representation of the x-axis from the left edge to the origin
Right(D)  Sequence describing the decimal representation of the x-axis from the origin to the right edge
             (an asterisk, "*", in an A-number indicates a near match)

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS

Rule	Left(B)	Right(B)	Left(D)	Right(D)
0,8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144, 152,160,168,176,184,192,200,208,216,224,232,240,248,256,264,272, 280,288,296,304,312,320,328,336,344,352,360,368,376,384,392,400, 408,416,424,432,440,448,456,464,472,480,488,496,504,512,520,528, 536,544,552,560,568,576,584,592,600,608,616,624,632,640,648,656, 664,672,680,688,696,704,712,720,728,736,744,752,760,768,776,784, 792,800,808,816,824,832,840,848,856,864,872,880,888,896,904,912, 920,928,936,944,952,960,968,976,984,992,1000,1008,1016	A000007	A000007	A000007	A000007
1,9,17,25,257,265,273,281	A277797	A277798	A277799	A277800
2,10,18,26,34,42,50,58,66,74,82,90,98,106,114,122,130,138,146, 154,162,170,178,186,194,202,210,218,226,234,242,250,258,266,274, 282,290,298,306,314,322,330,338,346,354,362,370,378,386,394,402, 410,418,426,434,442,450,458,466,474,482,490,498,506,514,522,530, 538,546,554,562,570,578,586,594,602,610,618,626,634,642,650,658, 666,674,682,690,698,706,714,722,730,738,746,754,762,770,778,786, 794,802,810,818,826,834,842,850,858,866,874,882,890,898,906,914, 922,930,938,946,954,962,970,978,986,994,1002,1010,1018	A000012	A011557	A000012	A000079
3,11,19,27,67,75,83,91	A277864	A277865	A277866	A277867
4,12,36,44,68,76,84,92,100,108,116,124,132,140,164,172,196,204, 212,220,228,236,244,252,516,524,548,556,580,588,596,604,612,620, 628,636,644,652,676,684,708,716,724,732,740,748,756,764	A277916	A277917	A277918	A101692*
5,13,21,29,37,45,53,61,69,77,85,93,101,109,117,125	A277926	A277927	A277928	A277929
6,38,70,86,102,134,166,198,230	A277931	A277932	A277933	A277934
7,15,23,31,39,47,55,63,71,79,87,95,103,111,119,127,135,143,151, 159,167,175,183,191,199,207,215,223,231,239,247,255,263,271,279, 287,295,303,311,319,327,335,343,351,359,367,375,383,391,399,407, 415,423,431,439,447,455,463,471,479,487,495,503,511	A277560	A277560	A277736	A277936
14,46,110,142,174,190,238,254	A277952	A277953	A277954	A277955
20,28,52,60,148,156,180,188,532,540,564,572,660,668,692,700	A273495	A273531	A273972	A273973
22	A274060	A274216	A274224	A274473
30	A274474	A274475	A274476	A274487
33	A276708	A276768	A276966	A277773
35	A278343	A278344	A278345	A278346
41	A278421	A278422	A278423	A278424
43,59	A278443	A278444	A278445	A278446
49	A278466	A278467	A278468	A278469
51	A278592	A278593	A278594	A278595
54	A278598	A278599	A278600	A278601
57	A278659	A278660	A278661	A278662
62	A278664	A278665	A278666	A278667
65,81,321,337	A278753	A278754	A278755	A278756
73,89	A278757	A278758	A278759	A278760
78	A278786	A278778	A278788	A278789
94	A278819	A278820	A278821	A278822
97	A278864	A278865	A278866	A278867
99	A278870	A278871	A278872	A278873
105	A278719	A278739	A278859	A278863
107	A278898	A278899	A278900	A278901
113	A278904	A278905	A278292	A278906
115	A278915	A278916	A278917	A278918
118	A278951	A278952	A278953	A278954
121	A278955	A278956	A278957	A278958
123	A278980	A279016	A279023	A279025
126	A272609	A273979	A274059	A274993
129,385	A279028	A279029	A279030	A279031
131,139,163,171,187,227,235,251	A279053	A056830*	A052992	A000975
133	A279137	A279138	A279139	A279140
137	A279141	A279142	A279143	A279144
141	A279145	A279146	A279147	A279148
145,153	A279149	A278584	A279150	A279151
147	A279173	A279174	A279175	A279176
150	A279246	A279247	A279248	A279249
155	A279250	A279251	A279252	A279253
157	A279468	A279469	A279470	A279471
158	A279472	A279473	A279474	A279475
161	A279498	A279499	A279500	A279501
165	A279502	A279503	A279504	A279505
169	A279545	A279546	A279547	A279548
173	A279597	A279598	A279599	A279600
177	A279601	A279602	A279603	A279604
179	A279528	A279665	A279666	A279668
181	A279669	A279670	A279671	A279672
182	A279694	A279695	A279696	A279697
185	A279698	A279699	A279700	A279701
189	A279716	A279717	A279718	A279719
193	A279720	A279721	A279722	A279723
195	A279748	A279749	A279750	A279751
197	A279752	A279753	A279754	A279755
201	A279799	A279800	A279801	A279802
203	A279808	A279809	A279810	A279811
205	A279822	A279823	A279824	A279825
206	A279826	A279827	A279828	A279829
209,465	A279118	A279118	A279872	A279872
211	A279873	A279874	A279875	A279876
213,245	A279877	A279878	A279879	A279880
214	A279936	A279937	A279938	A279939
217	A279940	A279941	A279942	A279943
219	A279057	A279123	A279957	A279958
221,253	A279959	A279960	A279961	A279962
222	A279949	A279985	A279986	A279987
225	A279988	A279989	A279990	A279991
229	A279992	A279993	A279994	A279995
233	A279996	A279997	A279998	A279999
237	A280137	A280138	A280139	A280140
241	A280141	A280142	A280143	A280144
243	A280145	A280146	A280147	A280148
246	A280329	A280330	A280331	A280332
249	A280334	A280335	A280336	A280337

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)

Rule	Left(B)	Right(B)	Left(D)	Right(D)
259,275	A280367	A280368	A280369	A280370
260,268,292,300,388,396,420,428,772,780,804,812,900,908,932,940	A280371	A280372	A280373	A280374
261,269,277,285,293,301,309,317,325,333,341,349,357,365,373,381	A280410	A280411	A280412	A051049
262	A280413	A280414	A280415	A280416
267	A280459	A280460	A280461	A280462
270	A280463	A280464	A280465	A280466
276,284,308,316,340,348,372,380,404,412,436,444,468,476,500,508, 773,781,788,789,796,797,820,828,837,845,852,853,860,861,884,892 ,916,924,948,956,980,988,1012,1020	A056830	A279053	A000975	A052992
278	A280365	A280524	A280525	A280526
283	A280527	A280528	A280529	A280530
286	A280561	A280562	A280563	A280564
289	A276708	A276768	A276966	A277773
291	A280565	A280566	A280567	A280568
294,422	A280606	A280607	A280608	A280609
297	A280612	A280613	A280614	A280615
299	A280833	A280834	A280835	A280836
302	A280837	A280838	A280839	A280840
305	A280973	A280974	A280975	A280976
307	A280977	A280978	A280979	A280980
310	A281035	A281036	A281037	A281038
313	A281039	A281040	A281041	A281042
315	A281043	A281044	A281045	A281046
318	A281088	A281099	A281100	A281101
323,339	A278753*	A278754*	A278755*	A278756*
324,332,356,364,452,460,484,492,836,844,868,876,964,972,996,1004	A281102	A281103	A281104	A281105
326	A281106	A281107	A281108	A281109
329	A281172	A281173	A281174	A281175
331	A281176	A281177	A281178	A281179
334	A280099	A280165	A281212	A281213
342	A281214	A281215	A281216	A281217
345	A281218	A281219	A281220	A281221
347	A281277	A281278	A281279	A281280
350	A281281	A281282	A281283	A281284
353	A281285	A281286	A281287	A281288
355	A281304	A281305	A281306	A281307
358	A281308	A281309	A281310	A281311
361	A281410	A281411	A281412	A281413
363	A281414	A281415	A281416	A281417
366	A281418	A281419	A281420	A281421
369	A281514	A281515	A281516	A281517
371	A281518	A281519	A281520	A281521
374	A281522	A281523	A281524	A281525
377	A281628	A281629	A281630	A281631
379	A281632	A281633	A281634	A281635
382	A281636	A281637	A281638	A281639
387	A281670	A281671	A281672	A281673
389	A281674	A281675	A281676	A281677
390	A281735	A281736	A281737	A281738
393	A281739	A281740	A281741	A281742
395	A281748	A281749	A281750	A281751
397	A281752	A281753	A281754	A281755
398	A281756	A281757	A281758	A281759
401,409,425	A281840	A281841	A281842	A281843
403	A281844	A281845	A281846	A281847
405	A281848	A281849	A281850	A281851
406	A281095	A281096	A281892	A281893
411	A281894	A281895	A281896	A281897
413,445,477,509	A282002	A282003	A282004	A282005
414	A282006	A282007	A282008	A282009
417	A282065	A282066	A282067	A282068
419	A282069	A282070	A282071	A282072
421	A282073	A282074	A282075	A282076
427	A282103	A282104	A282105	A282106
429	A282117	A282118	A282119	A282120
430	A282121	A282122	A282123	A282124
433	A282199	A282200	A282201	A282202
435	A282203	A282204	A282205	A282206
437	A282214	A282215	A282216	A282217
438	A282218	A282219	A282220	A282221
441	A282222	A282223	A282224	A282225
443	A282257	A282258	A282259	A282260
446	A282261	A282262	A282263	A282264
449	A282265	A282266	A282267	A282268
451	A282295	A282297	A282298	A282299
453	A282300	A282301	A282302	A282303
454	A282305	A282306	A282307	A282308

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)

Rule	Left(B)	Right(B)	Left(D)	Right(D)
457	A282359	A282360	A282361	A282362
459	A282363	A282364	A282365	A282366
461	A282367	A282368	A282369	A282370
462,510	A282385	A282386	A282387	A282388
467	A282411	A282412	A282413	A282414
469,501	A282415	A282416	A282417	A282418
470	A282419	A282420	A282421	A282422
473	A282447	A282428	A282429	A282450
475	A282451	A282452	A282453	A282454
478	A282482	A282483	A282484	A282485
481	A282486	A282487	A282488	A282489
483	A282490	A282491	A282492	A282493
485	A282276	A282325	A282514	A282553
486	A282602	A282603	A282604	A282605
489	A282606	A282607	A282608	A282609
491	A282652	A282653	A282654	A282655
493	A282656	A282657	A282658	A282659
494	A282660	A282661	A282662	A282663
497	A282674	A282675	A282676	A282677
499	A282678	A282679	A282680	A282681
502	A282682	A282683	A282684	A282685
505	A282796	A282797	A282798	A282799
507	A282800	A282801	A282802	A282803
513,561,769,817	A282804	A282805	A282806	A282807
515,523,547,555,571	A279053*	A281146	A052992*	A153772*
517	A281730	A282510	A282825	A282599
518,550,582,598,614	A273912	A273910	A038185	A273911
519,527,535,543,551,558,559,567,574,575,583,591,599,607,615,622, 623,631,638,639,647,655,663,671,679,686,687,695,702,703,711,719, 727,735,743,750,751,759,766,767,775,783,791,799,807,814,815,823, 830,831,839,847,855,863,871,878,879,887,894,895,903,911,919,927, 935,942,943,951,958,959,967,975,983,991,999,1006,1007,1015,1022, 1023	A002275*	A002275*	A000225*	A000225*
521	A282826	A282827	A282828	A282829
525	A282907	A282908	A282909	A282910
526	A282911	A282912	A282913	A282914
529,785	A282915	A282916	A282917	A282918
531	A282950	A282951	A282952	A282953
533	A282954	A282955	A282956	A282957
534	A282958	A282959	A282960	A282961
537	A282976	A282977	A282978	A282979
539	A282980	A282981	A282982	A282983
541	A282984	A282985	A282986	A282987
542	A283005	A283006	A283007	A283008
545	A283009	A283010	A283011	A283012
549	A283013	A283014	A283015	A283016
553	A282088	A282142	A282577	A282579
557	A282580	A282638	A282776	A283043
563	A283044	A283045	A283046	A283047
565	A283057	A283058	A283059	A283060
566	A283061	A283062	A283063	A283064
569	A283065	A283066	A283067	A283068
573	A283079	A283080	A283081	A283082
577	A283083	A283084	A283085	A283086
579	A283087	A283088	A283089	A283090
581	A283132	A283133	A283134	A283135
585	A283136	A283137	A283138	A283139
587	A283140	A283141	A283142	A283143
589	A283171	A283172	A283173	A283174
590	A283175	A283176	A283177	A283178
593	A283179	A283180	A283181	A283182
595	A283210	A283211	A283212	A283213
597	A283214	A283215	A283216	A283217
601	A283218	A283219	A283220	A283221
603	A283223	A283249	A283250	A283251
605	A283252	A283253	A283254	A283255
606	A283256	A283257	A283258	A283259
609	A283283	A283284	A283285	A283286
611	A283287	A283288	A283289	A283290
613	A283291	A283292	A283293	A283294
617	A282871	A283348	A283349	A283350
619,635	A283351	A283352	A140252*	A283353
621	A283355	A283356	A283357	A283358
625	A283372	A283373	A283374	A283375
627	A283376	A283377	A283378	A283379
629	A283387	A283388	A283389	A283390
630	A283396	A283397	A283398	A283399
633	A283400	A283401	A283402	A283403
637	A283404	A283405	A283406	A283407

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (concluded)

Rule	Left(B)	Right(B)	Left(D)	Right(D)
641,649,673,681,689,697,897,905	A283504	A283505	A283506	A283507
643,651,675,683,691,699,707,715,739,747,755,763	A267623	A283508	A036563	A153893*
645,653,661,669,677,685,693,701,709,717,725,733,741,749,757,765	A105279*	A002275*	A000918*	A000225*
646	A283581	A283582	A283583	A283584
654	A283585	A283586	A283587	A283588
657,665	A283589	A283590	A283591	A283592
659,667,723,731	A283596	A283597	A000225*	A000225*
662	A283600	A283601	A283602	A283603
670	A283604	A283605	A283606	A283607
678,742	A283641	A266508	A086893	A283642
694	A283644	A283645	A283646	A283647
705,713	A283648	A283649	A283650	A283651
710	A283699	A283700	A283701	A283702
718	A283703	A283704	A283705	A283706
721,729	A283707	A283708	A283709	A000225*
726	A283815	A283816	A283817	A283818
734	A283849	A283850	A283864	A283865
737,745,753,761,993,1001,1009,1017	A002275*	A002275*	A000225*	A000225*
758	A283712	A283713	A283752	A2837905
771,787,803,811,819,827,835,851,867,875,883,891	A283906	A283907	A283908	A283909
774	A283910	A283911	A283912	A283913
777	A283914	A283915	A283916	A283917
779,795,843,859	A284020	A284021	A284022	A284023
782	A284024	A284025	A284026	A284027
790,822,854,886	A284028	A284029	A283908*	A284031
793	A284083	A284084	A284085	A284086
798,862	A284087	A284088	A284022*	A284090
801	A284133	A284134	A284135	A284136
805,821,869,885	A284137	A284138	A284139	A284140
806	A284141	A284142	A284143	A284144
809	A284175	A284176	A284177	A284178
813,829,877,893	A284179	A284180	A284181	A284182
825	A284183	A284184	A284185	A284186
833,849	A284235	A284236	A284237	A284238
838	A284239	A284240	A284241	A284242
841,857	A284243	A284244	A284245	A284246
846	A284274	A284296	A284297	A284298
865,881	A284299	A284300	A284301	A284302
870	A284303	A284304	A284305	A284306
873,889	A284347	A284348	A284349	A284350
899,907,915,923,963,971,979,987	A284351	A284352	A284353	A284354
901,909,917,925,933,941,949,957,965,973,981,989,997,1005,1013,1021	A002275*	A002275*	A000225*	A000225*
902	A284355	A284356	A284357	A284358
910	A284399	A284400	A284401	A284402
913,921,929,937,945,953	A284403	A284404	A284405	A284406
918,982	A284407	A284408	A284409	A284410
926,990	A284419	A284420	A284421	A284422
931,939,947,955,995,1003,1011,1019	A002275*	A002275*	A000225*	A000225*
934	A284423	A284424	A284425	A284426
950,1014	A284479	A284480	A284481	A284482
961,977	A284483	A284484	A101622*	A284485
966	A284536	A284537	A284538	A284539
969,985	A002275*	A002275*	A000225*	A000225*
974	A284540	A284541	A284542	A284543
998	A284544	A284545	A284546	A284547

Sequences in the OEIS Related to 2D 5-Neighbor Outer Totalistic Cellular Automata Related to the Position of ON Cells Along the Diagonal

Column headings in the table below:

Rule    Wolfram's Rule Number(s) 
In(B)   Sequence describing the binary representation of the diagonal from a corner to the origin
Out(B)  Sequence describing the binary representation of the diagonal from the origin to a corner 
In(D)   Sequence describing the decimal representation of the diagonal from a corner to the origin
Out(D)  Sequence describing the decimal representation of the diagonal from the origin to a corner 
             (an asterisk, "*", in an A-number indicates a near match)

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS

Rule	In(B)	Out(B)	In(D)	Out(D)
0,4,8,12,16,24,32,36,40,44,48,56,64,68,72,76,80,88,96, 100,104,108,112,120,128,132,136,140,144,152,160,164,168,172, 176,184,192,196,200,204,208,216,224,228,232,236,240,248,256, 264,272,280,288,296,304,312,320,328,336,344,352,360,368,376, 384,392,400,408,416,424,432,440,448,456,464,472,480,488,496, 504,512,516,520,524,528,536,544,548,552,556,560,568,576,580, 584,588,592,600,608,612,616,620,624,632,640,644,648,652,656, 664,672,676,680,684,688,696,704,708,712,716,720,728,736,740, 744,748,752,760,768,776,784,792,800,808,816,824,832,840,848, 856,864,872,880,888,896,904,912,920,928,936,944,952,960,968, 976,984,992,1000,1008,1016	A000007	A000007	A000007	A000007
1,9,17,25,129,137,257,261,265,269,273,277,281,285,293,301, 309,317,325,333,337,341,345,349,357,365,373,381,385,393,401, 405,409,413,445,465,469,473,477,509	A280410	A280411	A280412	A280413
2,10,18,26,34,42,50,58,66,74,82,90,98,106,114,122,130,138, 146,154,162,170,178,186,194,202,210,218,226,234,242,250,258, 266,274,282,290,298,306,314,322,330,338,346,354,362,370,378, 386,394,402,410,418,426,434,442,450,458,466,474,482,490,498, 506,514,518,522,526,530,538,546,550,554,558,562,570,578,582, 586,590,594,602,610,614,618,622,626,634,642,646,650,654,658, 666,674,678,682,686,690,698,706,710,714,718,722,730,738,742, 746,750,754,762,770,778,786,794,802,810,818,826,834,842,850, 858,866,874,882,890,898,906,914,922,930,938,946,954,962,970, 978,986,994,1002,1010,1018	A000012	A011557	A000012	A000079
3,11,19,27,67,75,83,91	A285473	A285474	A080924	A285475
5,13,21,29,37,45,53,61,69,77,85,93,101,109,117,125	A277926	A277927	A277928	A277928
6,14,38,46,70,78,102,110,134,142,166,174,198,206,230,238	A019590	A285476	A019590	A130706
7,15,23,31,39,47,55,63,71,79,87,95,103,111,119,127,135, 143,151,159,167,175,183,191,199,207,215,223,231,239,247,255, 263,271,279,287,295,303,311,319,327,335,343,351,359,367,375, 383,391,399,407,415,423,431,439,447,455,463,471,479,487,495, 503,511	A277560	A277560	A277936	A277936
20,28,52,60,148,156,180,188,532,540,564,572,660,668,692, 700	A285477	A285478	A285479	A285480
22,86	A285434	A285435	A285436	A285437
30	A285536	A285637	A285538	A285539
33,289	A282415	A282416	A282417	A282418
35,43,59,163,171,227,235	A285540	A285541	A285542	A285543
41	A285544	A285545	A285546	A285547
49	A285556	A285557	A285558	A285559
51	A285560	A285561	A285562	A285563
54	A285608	A285609	A285610	A285611
57	A285604	A285605	A285606	A285607
62	A285612	A285613	A056453	A233411*
65,321	A285643	A285644	A285645	A285646
73	A285647	A285648	A285649	A285650
81	A285651	A285652	A285653	A285654
84,92,116,124,212,220,244,252,596,604,628,636,724,732,756, 764	A285771	A285772	A285773	A285774
89,145,153	A285775	A285776	A285777	A285778
94	A285780	A285781	A285782	A285783
97	A285816	A285817	A285818	A285819
99	A285820	A285821	A285822	A285823
105	A285825	A285826	A285827	A285828
107	A284940	A285833	A285834	A285835
113	A285837	A285838	A285839	A285840
115	A285841	A285842	A285843	A285844
118	A285897	A285907	A285908	A285909
121	A285910	A285911	A285912	A285913
123	A285945	A285946	A285947	A285948
126	A285941	A285942	A285943	A285944
131	A285xxx	A285xxx	A285xxx	A285xxx
133	A286018	A286019	A286020	A286021
139	A286022	A286023	A286024	A286025
141	A286026	A286027	A286028	A286029
147	A286078	A286079	A286080	A286081
149	A286082	A286083	A286084	A286085
150	A286086	A286087	A286088	A286089
155	A286112	A286113	A286114	A286115
157	A286116	A286117	A286118	A286119
158	A286120	A286121	A286122	A286123
161	A286136	A286140	A286165	A286166
165	A286167	A286168	A286169	A286170
169	A286171	A286172	A286173	A286174
173	A286196	A286197	A286198	A286199
177	A286200	A286201	A286202	A286203
179	A286204	A286205	A286206	A286207
181	A286403	A286404	A286405	A286406
182	A286407	A286408	A286409	A286410
185	A286411	A286412	A286413	A286414
187	A286498	A286500	A286501	A286502
189	A286503	A286504	A286505	A286506
190,254	A286507	A286508	A016116	A016116*
193	A286638	A286639	A286640	A286641
195	A286642	A286643	A286644	A286645
197	A286646	A286647	A286648	A286649
201	A286668	A286669	A286670	A286671
203	A286672	A286673	A286674	A286675
205	A286694	A286695	A286696	A286697
209	A286698	A286699	A286700	A286701
211	A286702	A286703	A286704	A286705
213	A286730	A286731	A286732	A286733
214	A286734	A286735	A286736	A286737
217	A286738	A286739	A286740	A286741
219	A286766	A286767	A286768	A286769
221	A286770	A286771	A286772	A286773
222	A286774	A286775	A286776	A286777
225	A286960	A286961	A286962	A286963
229	A283429	A286964	A286965	A286966
233	A286967	A286943	A286968	A286969
237	A287077	A287078	A287079	A287080
241	A287094	A287095	A287096	A287097
243	A287098	A287099	A287100	A287101
245	A287129	A287130	A287131	A287132
246	A287133	A287134	A287135	A287136
249	A287137	A287138	A287139	A287140
251	A286811	A287187	A287188	A287189
253	A287190	A287191	A287192	A287193

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)

Rule	In(B)	Out(B)	In(D)	Out(D)
259	A287194	A287196	A287197	A287199
260,268,292,300,388,396,420,428,772,780,804,812,900,908,932, 940	A287283	A287284	A287285	A287287
262	A287288	A287289	A287290	A287291
267	A287460	A287461	A287462	A287463
270	A287464	A287465	A287466	A287467
275	A280410*	A280411*	A280412*	A051049*
276,284,308,316,340,348,372,380,404,412,436,444,468,476,500, 508,788,796,820,828,852,860,884,892,916,924,948,956,980,988, 1012,1020	A287468	A287469	A077896	A287470
278	A287486	A287487	A287488	A287489
283	A287490	A287491	A287492	A287493
286	A287494	A287495	A287480	A287496
291	A287499	A287500	A287501	A287502
294	A287503	A287504	A287505	A287506
297	A287507	A287508	A287509	A287510
299	A287535	A287536	A287537	A287538
302	A287539	A287540	A287541	A287542
305	A287543	A287544	A287545	A287546
307	A286818	A286818	A287598	A287599
310	A287600	A287602	A287603	A287604
313	A287605	A287606	A287607	A287608
315	A287622	A287623	A287624	A287625
318	A287626	A287627	A287628	A287629
323	A285643*	A285644*	A285645*	A285646*
324,332,356,364,452,460,484,492,836,844,868,876,964,972,996,1004	A287630	A287631	A287632	A287633
326	A287710	A287711	A287712	A287713
329	A287714	A287715	A287716	A287717
331	A287718	A287719	A287720	A287721
334	A287734	A287735	A287736	A287737
339	A287738	A287739	A287740	A287741
342	A287742	A287743	A287744	A287745
347	A287749	A287750	A287751	A287752
350	A287753	A287754	A287755	A287756
353	A287757	A287758	A287759	A287760
355	A287778	A287779	A287780	A287781
358	A287782	A287783	A287784	A287785
361	A287786	A287787	A287788	A287789
363	A287848	A287849	A287850	A287851
366	A287852	A287853	A287854	A287855
369	A287856	A287857	A287858	A287859
371	A287902	A287903	A287904	A287905
374	A287906	A287907	A287908	A287909
377	A287910	A287911	A287912	A287913
379	A287941	A287942	A287946	A287947
382	A287948	A287949	A287950	A287951
387	A287952	A287953	A287954	A287955
389	A287975	A287976	A287977	A287978
390	A287979	A287980	A287981	A287982
395	A287983	A287984	A287985	A287986
397	A288008	A288009	A288010	A288011
398	A288012	A288013	A288014	A288015
403	A288016	A288017	A288018	A288019
406	A288042	A288043	A288044	A288045
411	A288046	A288047	A288048	A288049
414	A288050	A288051	A288052	A288053
417	A288056	A288057	A288058	A288059
419	A288060	A288061	A288062	A288063
421	A288064	A288065	A288066	A288067
422	A288121	A288123	A288124	A288125
425	A288127	A288128	A288129	A288130
427	A288131	A288136	A288137	A288138
429	A288190	A288191	A288192	A288193
430	A288194	A288195	A288196	A288197
433	A288198	A288200	A288201	A288202
435	A288292	A288293	A288294	A288295
437	A288296	A288297	A288298	A288299
438	A288300	A288301	A288302	A288303
441	A288328	A288329	A288330	A288331
443	A288332	A288333	A288334	A288335
446	A288336	A288337	A288338	A288339
449	A288357	A288358	A288359	A288360
451	A288361	A288362	A288363	A288364
453	A288365	A288366	A288367	A288368
454	A288393	A288394	A288395	A288396
457	A288397	A288398	A288399	A288400
459	A288401	A288402	A288403	A288404
461	A288431	A288432	A288433	A288434
462	A288435	A288436	A288437	A288438
467	A288439	A288440	A288441	A288442
470	A288494	A288495	A288496	A288497
475	A288498	A288499	A288500	A288501
478	A288503	A288504	A288505	A288506
481	A288584	A288585	A288586	A288587
483	A288588	A288589	A288590	A288591
485	A288592	A288593	A288594	A288595
486	A288642	A288643	A288644	A288645
489	A288646	A288647	A288648	A288649
491	A288650	A288651	A288652	A288653
493	A288661	A288662	A288663	A288664
494	A288697	A288698	A288699	A288700
497	A288701	A288702	A288704	A288705
499	A276540	A284040	A284041	A284042
501	A288020	A288761	A288762	A288763
502	A288764	A288765	A288766	A288767
505	A288768	A288769	A288770	A288771
507	A288801	A288802	A288803	A288804
510	A288805	A288806	A288807	A288808

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (concluded)

Rule	In(B)	Out(B)	In(D)	Out(D)
513,769
515,523
517
519,527,535,543,547,551,555,559,563,567,571,575,583,591,599, 607,611,615,619,623,627,631,635,639,647,655,663,671,675,679, 683,687,691,695,699,703,711,719,727,735,739,743,747,751,755, 759,763,767,775,783,791,799,803,807,811,815,819,823,827,831, 839,847,855,863,867,871,875,879,883,887,891,895,903,911,919, 927,931,935,939,943,947,951,955,959,967,975,983,991,995,999, 1003,1007,1011,1015,1019,1023
521
525
529
531
533
534
537
539
541
542
545
549
553
557
561
565
566,574,630,638,694,702,758,766,822,830,886,894,950,958,1014, 1022
569
573
577
579
581
585
587
589
593
595
597
598
601
603
605
606
609
613
617
621
625
629
633
637
641,649,897,905
643,651,707,715
645,653,661,669,677,685,693,701,709,717,725,733,741,749,757, 765
657,665
659,667,723,731
662
670
673,681,689,697
705,713
721,729
726
734
737,745,753,761,901,909,917,925,933,941,949,957,965,973,981, 989,993,997,1001,1005,1009,1013,1017,1021
771,787,835,851
773,781,789,797,837,845,853,861
774
777
779,795,843,859
782
785,793
790,854
798,862
801
805,821,869,885
806
809
813,829,877,893
814,942
817
825
833,849
838
841,857
846
865,881
870
873,889
878
899,907,915,923,963,971,979,987
902
910
913,921
918,982
926,990
929,937,945,953
934
961,977
966
969,985
974
998
1006

Mathematica Program To Generate the Sequences Above

(* Mathematica Program to Generate Outer Totalistic Cellular Automata Sequences *)
CAStep[rule_, a_] := Map[rule[ [10 - #] ] &, ListConvolve[{{0,2,0}, {2,1,2}, {0,2,0}}, a, 2], {2}];
code = 622; stages = 16;
rule = IntegerDigits[code, 2, 10];
(* Generate CA for this rule *)
g = 2*stages + 1;
a = PadLeft[{ {1} }, {g, g}, 0, Floor[{g, g}/2]];
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[ [1] ]] + 1)/2;
ca = Table[Table[Part[ca[ [n] ] [ [j] ], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n,1,k}];

"CA Evolution Diagrams"
lca = Length[ca];
For[is = 1, is ≤ lca, is++,
  Print["\nStage ", is - 1];
  c = ca[ [is] ];
  lc = Length[c];
  For[i = 1, i ≤ lc, i++,
    line = c[ [i] ];
    out = "";
    For[j = 1, j ≤ lc, j++, out = out <> If[line[ [j] ] == 0, " .", " x"]];
    Print[out];
  ]
];

"Counts of ON Cells at Each Stage"
on = Map[Function[Apply[Plus, Flatten[#1]]], ca]

"Counts of ON Cells at Stages 2^n-1"
Part[on, 2^Range[0, Log[2, stages]]]

"Partial Sums"
Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}]

"First Differences"
Table[on[ [i + 1] ] - on[ [i] ], {i, 1, Length[on] - 1}]

Output from the Mathematica Program To Generate the Sequences Above

CA Evolution Diagrams

Stage  0
 x

Stage  1
 . x .
 x x x
 . x .

Stage  2
 . . x . .
 . . x . .
 x x x x x
 . . x . .
 . . x . .

Stage  3
 . . . x . . .
 . . x x x . .
 . x . x . x .
 x x x x x x x
 . x . x . x .
 . . x x x . .
 . . . x . . .

Stage  4
 . . . . x . . . .
 . . . . x . . . .
 . . . x x x . . .
 . . x . x . x . .
 x x x x x x x x x
 . . x . x . x . .
 . . . x x x . . .
 . . . . x . . . .
 . . . . x . . . .


...


Stage  16
 . . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . .
 . . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . .
 . . . . . . . . . . . . . . . x x x . . . . . . . . . . . . . . .
 . . . . . . . . . . . . . . x x x x x . . . . . . . . . . . . . .
 . . . . . . . . . . . . . x x . x . x x . . . . . . . . . . . . .
 . . . . . . . . . . . . x x x . x . x x x . . . . . . . . . . . .
 . . . . . . . . . . . x x x x x x x x x x x . . . . . . . . . . .
 . . . . . . . . . . x x x . x x x x x . x x x . . . . . . . . . .
 . . . . . . . . . x x x x . x x x x x . x x x x . . . . . . . . .
 . . . . . . . . x . . x . x . x x x . x . x . . x . . . . . . . .
 . . . . . . . x x . . . x . . x x x . . x . . . x x . . . . . . .
 . . . . . . x x x x . . x x x x x x x x x . . x x x x . . . . . .
 . . . . . x x x x . x x . x . . x . . x . x x . x x x x . . . . .
 . . . . x x x . . x . x x . x x x x x . x x . x . . x x x . . . .
 . . . x x x x x x . . x . x . x x x . x . x . . x x x x x x . . .
 . . x x . . x x x x x x . x x . x . x x . x x x x x x . . x x . .
 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
 . . x x . . x x x x x x . x x . x . x x . x x x x x x . . x x . .
 . . . x x x x x x . . x . x . x x x . x . x . . x x x x x x . . .
 . . . . x x x . . x . x x . x x x x x . x x . x . . x x x . . . .
 . . . . . x x x x . x x . x . . x . . x . x x . x x x x . . . . .
 . . . . . . x x x x . . x x x x x x x x x . . x x x x . . . . . .
 . . . . . . . x x . . . x . . x x x . . x . . . x x . . . . . . .
 . . . . . . . . x . . x . x . x x x . x . x . . x . . . . . . . .
 . . . . . . . . . x x x x . x x x x x . x x x x . . . . . . . . .
 . . . . . . . . . . x x x . x x x x x . x x x . . . . . . . . . .
 . . . . . . . . . . . x x x x x x x x x x x . . . . . . . . . . .
 . . . . . . . . . . . . x x x . x . x x x . . . . . . . . . . . .
 . . . . . . . . . . . . . x x . x . x x . . . . . . . . . . . . .
 . . . . . . . . . . . . . . x x x x x . . . . . . . . . . . . . .
 . . . . . . . . . . . . . . . x x x . . . . . . . . . . . . . . .
 . . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . .
 . . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . .


Counts of ON Cells at Each Stage
{1,5,9,21,25,37,57,69,89,101,121,133,169,205,257,309,361}

Counts of ON Cells at Stages 2^n-1
{1,5,21,69,309}

Partial Sums
{1,6,15,36,61,98,155,224,313,414,535,668,837,1042,1299,1608,1969}

First Differences
{4,4,12,4,12,20,12,20,12,20,12,36,36,52,52,52}

Rules that generate equivalent counts of ON cells at stage 2^n-1

Rules in each of the lists below generate equivalent counts of ON cells at stage 2^n-1 based on the first 6 terms:

{0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432, 440, 448, 456, 464, 472, 480, 488, 496, 504, 512, 520, 528, 536, 544, 552, 560, 568, 576, 584, 592, 600, 608, 616, 624, 632, 640, 648, 656, 664, 672, 680, 688, 696, 704, 712, 720, 728, 736, 744, 752, 760, 768, 776, 784, 792, 800, 808, 816, 824, 832, 840, 848, 856, 864, 872, 880, 888, 896, 904, 912, 920, 928, 936, 944, 952, 960, 968, 976, 984, 992, 1000, 1008, 1016}

{1, 9, 17, 25, 257, 265, 273, 281, 673, 681, 689, 697}

{2, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114, 122, 130, 138, 146, 154, 162, 170, 178, 186, 194, 202, 210, 218, 226, 234, 242, 250, 258, 266, 274, 282, 290, 298, 306, 314, 322, 330, 338, 346, 354, 362, 370, 378, 386, 394, 402, 410, 418, 426, 434, 442, 450, 458, 466, 474, 482, 490, 498, 506, 514, 522, 530, 538, 546, 554, 562, 570, 578, 586, 594, 602, 610, 618, 626, 634, 642, 650, 658, 666, 674, 682, 690, 698, 706, 714, 722, 730, 738, 746, 754, 762, 770, 778, 786, 794, 802, 810, 818, 826, 834, 842, 850, 858, 866, 874, 882, 890, 898, 906, 914, 922, 930, 938, 946, 954, 962, 970, 978, 986, 994, 1002, 1010, 1018}

{3, 11, 19, 27, 67, 75, 83, 91, 675, 683, 691, 699, 739, 747, 755, 763, 899, 907, 915, 923, 963, 971, 979, 987}

{4, 12, 36, 44, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 164, 172, 196, 204, 212, 220, 228, 236, 244, 252, 276, 284, 308, 316, 340, 348, 372, 380, 404, 412, 436, 444, 468, 476, 500, 508, 516, 524, 548, 556, 580, 588, 596, 604, 612, 620, 628, 636, 644, 652, 676, 684, 708, 716, 724, 732, 740, 748, 756, 764, 788, 796, 820, 828, 852, 860, 884, 892, 916, 924, 948, 956, 980, 988, 1012, 1020}

{5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 125, 901, 909, 917, 925, 933, 941, 949, 957, 965, 973, 981, 989, 997, 1005, 1013, 1021}

{6, 38, 70, 102, 134, 166, 198, 230}

{7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 119, 127, 135, 143, 151, 159, 167, 175, 183, 191, 199, 207, 215, 223, 231, 239, 247, 255, 263, 271, 279, 287, 295, 303, 311, 319, 327, 335, 343, 351, 359, 367, 375, 383, 391, 399, 407, 415, 423, 431, 439, 447, 455, 463, 471, 479, 487, 495, 503, 511, 519, 527, 535, 543, 551, 559, 567, 575, 583, 591, 599, 607, 615, 623, 631, 639, 647, 655, 663, 671, 679, 687, 695, 703, 711, 719, 727, 735, 743, 751, 759, 767, 775, 783, 791, 799, 807, 815, 823, 831, 839, 847, 855, 863, 871, 879, 887, 895, 903, 911, 919, 927, 935, 943, 951, 959, 967, 975, 983, 991, 999, 1007, 1015, 1023}

{14, 46, 142, 174}

{20, 28, 52, 60, 148, 156, 180, 188, 532, 540, 564, 572, 660, 668, 692, 700}

{35, 43, 59}

{65, 321}

{86, 342}

{129, 385, 425, 465, 553}

{131, 163, 171, 227, 235, 771, 787, 803, 811, 819, 827, 835, 851, 867, 875, 883, 891}

{145, 153}

{190, 254}

{221, 253}

{245, 501}

{260, 268, 292, 300, 388, 396, 420, 428, 772, 780, 804, 812, 900, 908, 932, 940}

{261, 269, 277, 285, 293, 301, 309, 317, 325, 333, 341, 349, 357, 365, 373, 381, 413, 445, 477, 509, 645, 653, 661, 669, 677, 685, 693, 701, 709, 717, 725, 733, 741, 749, 757, 765}

{324, 332, 356, 364, 452, 460, 484, 492, 836, 844, 868, 876, 964, 972, 996, 1004}

{337, 505}

{401, 409}

{430, 558, 598, 686, 750, 926, 990}

{510, 574, 638, 702, 766, 790, 830, 854, 894, 958, 1022}

{513, 769}

{515, 523}

{518, 550, 582, 614

{555, 571}

{619, 635}

{641, 649, 897, 905}

{643, 651, 707, 715}

{657, 665}

{659, 667, 723, 731, 931, 939, 947, 955, 995, 1003, 1011, 1019}

{705, 713}

{721, 729}

{737, 745, 753, 761, 993, 1001, 1009, 1017}

{773, 781, 789, 797, 837, 845, 853, 861}

{779, 795, 843, 859}

{798, 862}

{805, 821, 869, 885}

{813, 829, 877, 893}

{822, 886}

{833, 849}

{841, 857}

{865, 881}

{873, 889}

{913, 921, 929, 937, 945, 953}

{918, 982}

{950, 1014}

{961, 977}

{969, 985}

Links

• N. J. A. Sloane, On the Number of ON Cells in Cellular Automata
• Eric Weisstein's World of Mathematics, Cellular Automaton
• Eric Weisstein's World of Mathematics, Outer Totalistic Cellular Automaton
• Eric Weisstein's World of Mathematics, Totalistic Cellular Automaton
• WolframAlpha, Outer Totalistic Cellular Automaton
• S. Wolfram, A New Kind of Science
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index to Elementary Cellular Automata
• OEIS Index entries for sequences related to cellular automata