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A269568 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood.

%I A269568 #11 Feb 16 2025 08:33:30
%S A269568 4,4,12,4,12,20,12,20,12,20,12,36,36,52,52,52,-28,44,4,4,76,4,44,92,
%T A269568 52,44,84,108,-44,252,-20,276,-148,100,44,-4,12,-36,116,116,36,12,108,
%U A269568 20,84,124,132,292,-180,212,-12,132,12,300,228,52,196,148,36,276
%N A269568 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood.
%C A269568 Initialized with a single black (ON) cell at stage zero.
%D A269568 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A269568 Robert Price, <a href="/A269568/b269568.txt">Table of n, a(n) for n = 0..299</a>
%H A269568 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, 2015
%H A269568 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269568 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269568 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269568 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A269568 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A269568 rule=622; stages=300; ca=CellularAutomaton[ {rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}}, {{{1}},0}, stages]; (* Start with single black cell *) on=Map[Function[Apply[Plus,Flatten[#1]]],ca]; (* Count ON cells at each stage *) Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}]
%Y A269568 Cf. A269522.
%K A269568 sign,easy
%O A269568 0,1
%A A269568 _Robert Price_, Feb 29 2016