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A269717 Partial sums of the 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 A269717 #11 Feb 16 2025 08:33:30
%S A269717 1,6,14,34,50,94,126,214,246,338,402,586,650,834,962,1330,1394,1582,
%T A269717 1710,2086,2214,2590,2846,3598,3726,4102,4358,5110,5366,6118,6630,
%U A269717 8134,8262,8642,8898,9658,9914,10674,11186,12706,12962,13722,14234,15754,16266
%N A269717 Partial sums of the 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 A269717 Initialized with a single black (ON) cell at stage zero.
%D A269717 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A269717 Robert Price, <a href="/A269717/b269717.txt">Table of n, a(n) for n = 0..300</a>
%H A269717 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 A269717 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269717 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269717 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269717 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A269717 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A269717 rule=22; stages=300;
%t A269717 ca=CellularAutomaton[{rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}},{{{1}},0},stages]; (* Start with single black cell *)
%t A269717 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t A269717 Table[Total[Part[on,Range[1,i]]],{i,1,Length[on]}] (* Sum at each stage *)
%Y A269717 Cf. A269715.
%K A269717 nonn,easy
%O A269717 0,2
%A A269717 _Robert Price_, Mar 04 2016