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 A280144 Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 241", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 7, 0, 31, 0, 127, 0, 511, 64, 1919, 256, 8191, 1088, 32639, 4864, 120319, 20032, 513919, 107264, 2039295, 52800, 8271743, 1291008, 32833023, 7228992, 130144127, 25146112, 511802879, 24694336, 2118080383, 730018560, 8329199103, 772574784, 31203383167 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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 = 241; 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]]] + 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]], 2], {i , 1, stages - 1}] CROSSREFS Cf. A280141, A280142, A280143. Sequence in context: A282680 A282677 A280143 * A157779 A222322 A228762 Adjacent sequences:  A280141 A280142 A280143 * A280145 A280146 A280147 KEYWORD nonn,easy AUTHOR Robert Price, Dec 26 2016 STATUS approved

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Last modified January 23 11:59 EST 2022. Contains 350512 sequences. (Running on oeis4.)