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%I A278980 #21 Dec 05 2016 16:21:28
%S A278980 1,1,1,1111,100,110111,0,11111111,10000,1111010111,10000,111111110111,
%T A278980 1000000,11111101011111,1000000,1111111111111111,101010000,
%U A278980 111111110101010111,101010000,11111111111111010111,10000010000,1111111111010111110111,10001000000,111111111111111101111111,1010100010000
%N A278980 Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 123", based on the 5-celled von Neumann neighborhood.
%C A278980 Initialized with a single black (ON) cell at stage zero.
%C A278980 Differs from A278915 for example at a(24). - _Robert Price_, Dec 05 2016
%D A278980 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A278980 Robert Price, <a href="/A278980/b278980.txt">Table of n, a(n) for n = 0..126</a>
%H A278980 Robert Price, <a href="/A278980/a278980.tmp.txt">Diagrams of first 20 stages</a>
%H A278980 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 A278980 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A278980 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A278980 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A278980 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A278980 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A278980 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A278980 Robert Price, <a href="/A278980/a278980.tmp.txt">Diagrams of first 20 stages</a>
%t A278980 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A278980 code = 123; stages = 128;
%t A278980 rule = IntegerDigits[code, 2, 10];
%t A278980 g = 2 * stages + 1; (* Maximum size of grid *)
%t A278980 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A278980 ca = a;
%t A278980 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A278980 PrependTo[ca, a];
%t A278980 (* Trim full grid to reflect growth by one cell at each stage *)
%t A278980 k = (Length[ca[[1]]] + 1)/2;
%t A278980 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 A278980 Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 10], {i, 1, stages - 1}]
%Y A278980 Cf. A279016, A279023, A279025.
%K A278980 nonn,easy
%O A278980 0,4
%A A278980 _Robert Price_, Dec 03 2016
%E A278980 Added a(23) and a(24) to distinguish the sequence from A278915. - _Robert Price_, Dec 05 2016

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