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%I #12 Mar 17 2016 04:09:57
%S 1,5,12,20,32,32,64,52,104,60,152,108,200,176,268,236,328,260,452,292,
%T 520,388,656,480,784,516,908,648,1096,724,1204,916,1240,1000,1452,
%U 1088,1532,1316,1792,1368,1976,1636,2208,1732,2280,2208,2292,2272,2612,2528
%N Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 158", based on the 5-celled von Neumann neighborhood.
%C Initialized with a single black (ON) cell at stage zero.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H Robert Price, <a href="/A270333/b270333.txt">Table of n, a(n) for n = 0..128</a>
%H Robert Price, <a href="/A270333/a270333.tmp.txt">Diagrams of the first 20 stages.</a>
%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t code=158; stages=128;
%t rule=IntegerDigits[code,2,10];
%t g=2*stages+1; (* Maximum size of grid *)
%t a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t ca=a;
%t ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t PrependTo[ca,a];
%t (* Trim full grid to reflect growth by one cell at each stage *)
%t k=(Length[ca[[1]]]+1)/2;
%t 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 Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t Total[#, 2] & /@ CellularAutomaton[{158, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, {20}] (* _JungHwan Min_, Mar 16 2016 *)
%K nonn,easy
%O 0,2
%A _Robert Price_, Mar 15 2016
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