%I #17 Jul 26 2024 21:16:33
%S 1,5,20,52,236,916,4060,16904,66660,265800,1059724,4219684,16816424,
%T 67131892,268216416,1072151796
%N Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 158", based on the 5-celled von Neumann neighborhood.
%C Initialized with a single black (ON) cell at stage zero.
%D Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%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 Stephen 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 (* From _Robert Price_, Start *)
%t CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
%t code = 158; stages = 128;
%t rule = IntegerDigits[code, 2, 10];
%t g = 2 * stages + 1; (* Maximum size of grid *)
%t a = PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t ca = a;
%t ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t PrependTo[ca, a];
%t (* Trim full grid to reflect growth by one cell at each stage *)
%t k = (Length[ca[[1]]] + 1)/2;
%t ca = Table[Table[Part[ca[[n]][[j]], Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1 ,k}];
%t on = Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
%t Part[on, 2^Range[0, Log[2, stages]]] (* Extract relevant terms *)
%t (* From _Robert Price_, End *)
%t Total[#, 2] & /@ Array[CellularAutomaton[{158, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, {{{2^# - 1}}}] &, 6] (* _JungHwan Min_, Mar 16 2016 *)
%Y Cf. A270333.
%K nonn,more
%O 0,2
%A _Robert Price_, Mar 15 2016
%E a(8)-a(15) from _Lars Blomberg_, May 07 2016
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