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%I A270946 #11 Jul 26 2024 21:16:35
%S A270946 1,8,4,40,17,104,20,189,52,324,72,465,96,648,97,812,204,1101,164,1352,
%T A270946 272,1632,264,1953,380,2376,473,2708,476,3109,528,3540,677,4060,773,
%U A270946 4448,808,5053,888,5604,973,6248,1157,6840,1248,7521,1316,8028,1377,8880
%N A270946 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 229", based on the 5-celled von Neumann neighborhood.
%C A270946 Initialized with a single black (ON) cell at stage zero.
%D A270946 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A270946 Robert Price, <a href="/A270946/b270946.txt">Table of n, a(n) for n = 0..128</a>
%H A270946 Robert Price, <a href="/A270946/a270946.tmp.txt">Diagrams of the first 20 stages.</a>
%H A270946 N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015
%H A270946 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A270946 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A270946 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A270946 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A270946 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A270946 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t A270946 code=229; stages=128;
%t A270946 rule=IntegerDigits[code,2,10];
%t A270946 g=2*stages+1; (* Maximum size of grid *)
%t A270946 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t A270946 ca=a;
%t A270946 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t A270946 PrependTo[ca,a];
%t A270946 (* Trim full grid to reflect growth by one cell at each stage *)
%t A270946 k=(Length[ca[[1]]]+1)/2;
%t A270946 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 A270946 Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%K A270946 nonn,easy
%O A270946 0,2
%A A270946 _Robert Price_, Mar 26 2016

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