# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a270844 Showing 1-1 of 1 %I A270844 #42 Jul 26 2024 21:16:35 %S A270844 4,4,15,-3,51,-27,67,-19,131,-107,203,-147,291,-259,323,-235,559,-627, %T A270844 875,-955,1355,-1131,1027,-787,1163,-1175,1403,-1339,1751,-1623,1603, %U A270844 -1359,2003,-2191,2800,-2960,3363,-2891,3111,-3083,3727,-3667,3944,-3560,4027 %N A270844 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 451", based on the 5-celled von Neumann neighborhood. %C A270844 Initialized with a single black (ON) cell at stage zero. %D A270844 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. %H A270844 Robert Price, Table of n, a(n) for n = 0..127 %H A270844 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 %H A270844 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A270844 S. Wolfram, A New Kind of Science %H A270844 Index entries for sequences related to cellular automata %H A270844 Index to 2D 5-Neighbor Cellular Automata %H A270844 Index to Elementary Cellular Automata %t A270844 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}]; %t A270844 code=451; stages=128; %t A270844 rule=IntegerDigits[code,2,10]; %t A270844 g=2*stages+1; (* Maximum size of grid *) %t A270844 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *) %t A270844 ca=a; %t A270844 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}]; %t A270844 PrependTo[ca,a]; %t A270844 (* Trim full grid to reflect growth by one cell at each stage *) %t A270844 k=(Length[ca[[1]]]+1)/2; %t A270844 ca=Table[Table[Part[ca[[n]][[j]],Range[k+1-n,k-1+n]],{j,k+1-n,k-1+n}],{n,1,k}]; %t A270844 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *) %t A270844 Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}] (* Difference at each stage *) %Y A270844 Cf. A272256. %K A270844 sign,easy %O A270844 0,1 %A A270844 _Robert Price_, Apr 23 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE