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A269567 Partial sums of the 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 A269567 #9 Feb 16 2025 08:33:30
%S A269567 1,6,15,36,61,98,155,224,313,414,535,668,837,1042,1299,1608,1969,2302,
%T A269567 2679,3060,3445,3906,4371,4880,5481,6134,6831,7612,8501,9346,10443,
%U A269567 11520,12873,14078,15383,16732,18077,19434,20755,22192,23745,25334,26935,28644
%N A269567 Partial sums of the 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 A269567 Initialized with a single black (ON) cell at stage zero.
%D A269567 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A269567 Robert Price, <a href="/A269567/b269567.txt">Table of n, a(n) for n = 0..300</a>
%H A269567 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 A269567 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269567 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269567 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269567 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A269567 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A269567 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[Total[Part[on,Range[1,i]]],{i,1,Length[on]}]
%Y A269567 Cf. A269522.
%K A269567 nonn,easy
%O A269567 0,2
%A A269567 _Robert Price_, Feb 29 2016