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A269713 Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 20", based on the 5-celled von Neumann neighborhood.

%I A269713 #13 Feb 16 2025 08:33:30
%S A269713 1,5,13,25,45,69,113,141,193,249,353,409,513,625,837,897,1013,1133,
%T A269713 1365,1485,1717,1957,2421,2541,2773,3013,3477,3717,4181,4661,5593,
%U A269713 5717,5961,6209,6697,6945,7433,7929,8905,9153,9641,10137,11113,11609,12585,13577
%N A269713 Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 20", based on the 5-celled von Neumann neighborhood.
%C A269713 Initialized with a single black (ON) cell at stage zero.
%C A269713 Rules 28, 52, 60, 148, 156, 180, 188, 532, 540, 564, 572, 660, 668, 692 and 700 also generate this sequence.
%D A269713 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A269713 Robert Price, <a href="/A269713/b269713.txt">Table of n, a(n) for n = 0..300</a>
%H A269713 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 A269713 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269713 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269713 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269713 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A269713 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A269713 rule=20; stages=300;
%t A269713 ca=CellularAutomaton[{rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}},{{{1}},0},stages]; (* Start with single black cell *)
%t A269713 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t A269713 Table[Total[Part[on,Range[1,i]]],{i,1,Length[on]}] (* Sum at each stage *)
%Y A269713 Cf. A269711.
%K A269713 nonn,easy
%O A269713 0,2
%A A269713 _Robert Price_, Mar 04 2016