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%I A280975 #8 Jan 12 2017 16:02:37
%S A280975 1,0,1,12,1,60,1,252,9,1000,27,4036,17,16324,21,65498,165,261702,17,
%T A280975 1048516,917,4192542,333,16776322,2105,67101584,2327,268427592,3203,
%U A280975 1073733688,3987,4294959872,2175,17179863852,7217,68719462788,32821,274877792138,38189
%N A280975 Decimal 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 305", based on the 5-celled von Neumann neighborhood.
%C A280975 Initialized with a single black (ON) cell at stage zero.
%D A280975 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A280975 Robert Price, <a href="/A280975/b280975.txt">Table of n, a(n) for n = 0..126</a>
%H A280975 Robert Price, <a href="/A280975/a280975.tmp.txt">Diagrams of first 20 stages</a>
%H A280975 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 A280975 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A280975 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A280975 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A280975 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A280975 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A280975 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A280975 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A280975 code = 305; stages = 128;
%t A280975 rule = IntegerDigits[code, 2, 10];
%t A280975 g = 2 * stages + 1; (* Maximum size of grid *)
%t A280975 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A280975 ca = a;
%t A280975 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A280975 PrependTo[ca, a];
%t A280975 (* Trim full grid to reflect growth by one cell at each stage *)
%t A280975 k = (Length[ca[[1]]] + 1)/2;
%t A280975 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 A280975 Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 2], {i, 1, stages - 1}]
%Y A280975 Cf. A280973, A280974, A280976.
%K A280975 nonn,easy
%O A280975 0,4
%A A280975 _Robert Price_, Jan 11 2017

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