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%I A281108 #7 Jan 15 2017 11:50:47
%S A281108 1,3,4,14,17,59,68,238,257,899,1092,3822,4113,14395,17472,61152,65808,
%T A281108 230328,279556,978446,1052945,3685307,4473924,15658734,16842769,
%U A281108 58949691,71581764,250536174,269553937,943438779,1145061444,4007715054,4312862993,15095020475
%N A281108 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 326", based on the 5-celled von Neumann neighborhood.
%C A281108 Initialized with a single black (ON) cell at stage zero.
%D A281108 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A281108 Robert Price, <a href="/A281108/b281108.txt">Table of n, a(n) for n = 0..126</a>
%H A281108 Robert Price, <a href="/A281108/a281108.tmp.txt">Diagrams of first 20 stages</a>
%H A281108 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 A281108 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A281108 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A281108 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A281108 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A281108 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A281108 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A281108 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A281108 code = 326; stages = 128;
%t A281108 rule = IntegerDigits[code, 2, 10];
%t A281108 g = 2 * stages + 1; (* Maximum size of grid *)
%t A281108 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A281108 ca = a;
%t A281108 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A281108 PrependTo[ca, a];
%t A281108 (* Trim full grid to reflect growth by one cell at each stage *)
%t A281108 k = (Length[ca[[1]]] + 1)/2;
%t A281108 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 A281108 Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 2], {i, 1, stages - 1}]
%Y A281108 Cf. A281106, A281107, A281109.
%K A281108 nonn,easy
%O A281108 0,2
%A A281108 _Robert Price_, Jan 14 2017

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