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%I A288294 #7 Jun 07 2017 19:15:54
%S A288294 1,3,3,14,3,60,15,255,12,1011,30,4095,15,16371,206,65531,247,261950,
%T A288294 487,1048472,231,4194076,1763,16776988,1787,67108614,8185,268435006,
%U A288294 8159,1073741728,52319,4294967231,61388,17179811775,127939,68719476734,903,274877906424
%N A288294 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 435", based on the 5-celled von Neumann neighborhood.
%C A288294 Initialized with a single black (ON) cell at stage zero.
%D A288294 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A288294 Robert Price, <a href="/A288294/b288294.txt">Table of n, a(n) for n = 0..126</a>
%H A288294 Robert Price, <a href="/A288294/a288294.tmp.txt">Diagrams of first 20 stages</a>
%H A288294 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 A288294 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A288294 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A288294 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A288294 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A288294 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A288294 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A288294 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A288294 code = 435; stages = 128;
%t A288294 rule = IntegerDigits[code, 2, 10];
%t A288294 g = 2 * stages + 1; (* Maximum size of grid *)
%t A288294 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A288294 ca = a;
%t A288294 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A288294 PrependTo[ca, a];
%t A288294 (* Trim full grid to reflect growth by one cell at each stage *)
%t A288294 k = (Length[ca[[1]]] + 1)/2;
%t A288294 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 A288294 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]
%Y A288294 Cf. A288292, A288293, A288295.
%K A288294 nonn,easy
%O A288294 0,2
%A A288294 _Robert Price_, Jun 07 2017

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