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%I #9 May 02 2016 17:47:13
%S 1,8,5,44,17,112,29,204,61,336,73,492,109,672,157,876,229,1136,241,
%T 1420,277,1728,329,2044,429,2432,477,2812,573,3264,633,3652,861,4168,
%U 873,4708,909,5272,961,5844,1061,6488,1113,7108,1237,7800,1353,8388,1645
%N Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 493", 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="/A272543/b272543.txt">Table of n, a(n) for n = 0..128</a>
%H Robert Price, <a href="/A272543/a272543.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>
%H Robert Price, <a href="/A272543/a272543.tmp.txt">Diagrams of the first 20 stages</a>
%t CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t code=493; 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 *)
%K nonn,easy
%O 0,2
%A _Robert Price_, May 02 2016
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