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A269697 Partial sums of the 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 A269697 #13 Feb 16 2025 08:33:30
%S A269697 1,6,10,30,34,54,70,150,154,174,190,270,286,366,430,750,754,774,790,
%T A269697 870,886,966,1030,1350,1366,1446,1510,1830,1894,2214,2470,3750,3754,
%U A269697 3774,3790,3870,3886,3966,4030,4350,4366,4446,4510,4830,4894,5214,5470,6750
%N A269697 Partial sums of the 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 A269697 Initialized with a single black (ON) cell at stage zero.
%C A269697 Rules 38, 70, 102, 134, 166, 198 and 230 also generate this sequence.
%D A269697 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A269697 Robert Price, <a href="/A269697/b269697.txt">Table of n, a(n) for n = 0..300</a>
%H A269697 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 A269697 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269697 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269697 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269697 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A269697 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A269697 rule=6; stages=300;
%t A269697 ca=CellularAutomaton[{rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}},{{{1}},0},stages]; (* Start with single black cell *)
%t A269697 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t A269697 Table[Total[Part[on,Range[1,i]]],{i,1,Length[on]}] (* Sum at each stage *)
%Y A269697 Cf. A269695.
%K A269697 nonn,easy
%O A269697 0,2
%A A269697 _Robert Price_, Mar 03 2016