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 A286118 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 157", based on the 5-celled von Neumann neighborhood. 4
 1, 2, 0, 14, 1, 62, 0, 255, 0, 1022, 0, 4094, 1, 16382, 0, 65526, 9, 262134, 8, 1048566, 9, 4194278, 16, 16777190, 25, 67108838, 24, 268435424, 31, 1073741696, 79, 4294967216, 72, 17179869108, 8, 68719476615, 112, 274877906447, 432, 1099511627343, 432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Initialized with a single black (ON) cell at stage zero. REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. LINKS Robert Price, Table of n, a(n) for n = 0..126 Robert Price, Diagrams of first 20 stages N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science Wolfram Research, Wolfram Atlas of Simple Programs MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 157; stages = 128; rule = IntegerDigits[code, 2, 10]; g = 2 * stages + 1; (* Maximum size of grid *) a = PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *) ca = a; ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}]; PrependTo[ca, a]; (* Trim full grid to reflect growth by one cell at each stage *) k = (Length[ca[]] + 1)/2; ca = Table[Table[Part[ca[[n]] [[j]], Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}]; Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}] CROSSREFS Cf. A286116, A286117, A286119. Sequence in context: A293936 A110685 A225480 * A286084 A286732 A286772 Adjacent sequences:  A286115 A286116 A286117 * A286119 A286120 A286121 KEYWORD nonn,easy AUTHOR Robert Price, May 02 2017 STATUS approved

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Last modified June 24 04:38 EDT 2019. Contains 324318 sequences. (Running on oeis4.)