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A269718 First differences of 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 A269718 #16 Feb 16 2025 08:33:30
%S A269718 4,3,12,-4,28,-12,56,-56,60,-28,120,-120,120,-56,240,-304,124,-60,248,
%T A269718 -248,248,-120,496,-624,248,-120,496,-496,496,-240,992,-1376,252,-124,
%U A269718 504,-504,504,-248,1008,-1264,504,-248,1008,-1008,1008,-496,2016,-2784
%N A269718 First differences of 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 A269718 Initialized with a single black (ON) cell at stage zero.
%D A269718 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A269718 Robert Price, <a href="/A269718/b269718.txt">Table of n, a(n) for n = 0..299</a>
%H A269718 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 A269718 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269718 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269718 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269718 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A269718 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A269718 rule=22; stages=300;
%t A269718 ca=CellularAutomaton[{rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}},{{{1}},0},stages]; (* Start with single black cell *)
%t A269718 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t A269718 Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}] (* Difference at each stage *)
%Y A269718 Cf. A269715.
%K A269718 sign,easy
%O A269718 0,1
%A A269718 _Robert Price_, Mar 04 2016