%I #15 Mar 11 2016 04:00:04
%S 1,4,8,12,20,24,44,28,52,56,104,56,104,112,212,60,116,120,232,120,232,
%T 240,464,120,232,240,464,240,464,480,932,124,244,248,488,248,488,496,
%U 976,248,488,496,976,496,976,992,1952,248,488,496,976,496,976,992
%N 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 Initialized with a single black (ON) cell at stage zero.
%C Rules 28, 52, 60, 148, 156, 180, 188, 532, 540, 564, 572, 660, 668, 692 and 700 also generate this sequence.
%C Apparently a duplicate of A122108. - _R. J. Mathar_, Mar 09 2016
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H Robert Price, <a href="/A269711/b269711.txt">Table of n, a(n) for n = 0..300</a>
%H Robert Price, <a href="/A269711/a269711.tmp.txt">Diagrams of first 20 stages.</a>
%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t rule=20; stages=300;
%t ca=CellularAutomaton[{rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}},{{{1}},0},stages]; (* Start with single black cell *)
%t Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%K nonn,easy
%O 0,2
%A _Robert Price_, Mar 04 2016
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