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A269715 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 22", based on the 5-celled von Neumann neighborhood.

%I A269715 #12 Feb 16 2025 08:33:30
%S A269715 1,5,8,20,16,44,32,88,32,92,64,184,64,184,128,368,64,188,128,376,128,
%T A269715 376,256,752,128,376,256,752,256,752,512,1504,128,380,256,760,256,760,
%U A269715 512,1520,256,760,512,1520,512,1520,1024,3040,256,760,512,1520,512
%N A269715 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 22", based on the 5-celled von Neumann neighborhood.
%C A269715 Initialized with a single black (ON) cell at stage zero.
%D A269715 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A269715 Robert Price, <a href="/A269715/b269715.txt">Table of n, a(n) for n = 0..300</a>
%H A269715 Robert Price, <a href="/A269715/a269715.tmp.txt">Diagrams of the first 20 stages.</a>
%H A269715 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 A269715 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269715 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269715 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269715 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A269715 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A269715 rule=22; stages=300;
%t A269715 ca=CellularAutomaton[{rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}},{{{1}},0},stages]; (* Start with single black cell *)
%t A269715 Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%K A269715 nonn,easy
%O A269715 0,2
%A A269715 _Robert Price_, Mar 04 2016