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A269695 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 6", based on the 5-celled von Neumann neighborhood.

%I A269695 #15 Feb 16 2025 08:33:30
%S A269695 1,5,4,20,4,20,16,80,4,20,16,80,16,80,64,320,4,20,16,80,16,80,64,320,
%T A269695 16,80,64,320,64,320,256,1280,4,20,16,80,16,80,64,320,16,80,64,320,64,
%U A269695 320,256,1280,16,80,64,320,64,320,256,1280,64,320,256,1280,256
%N A269695 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 6", based on the 5-celled von Neumann neighborhood.
%C A269695 Initialized with a single black (ON) cell at stage zero.
%C A269695 Rules 38, 70, 102, 134, 166, 198 and 230 also generate this sequence.
%D A269695 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A269695 Robert Price, <a href="/A269695/b269695.txt">Table of n, a(n) for n = 0..300</a>
%H A269695 Robert Price, <a href="/A269695/a269695.tmp.txt">Diagrams of first 20 stages</a>
%H A269695 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 A269695 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269695 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269695 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269695 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A269695 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A269695 rule=6; stages=300;
%t A269695 ca=CellularAutomaton[{rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}},{{{1}},0},stages]; (* Start with single black cell *)
%t A269695 Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%K A269695 nonn,easy
%O A269695 0,2
%A A269695 _Robert Price_, Mar 03 2016