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 A286406 Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 181", based on the 5-celled von Neumann neighborhood. 4
 1, 1, 0, 7, 24, 15, 96, 63, 192, 1023, 256, 4095, 0, 16383, 0, 53247, 61440, 212991, 114688, 1015807, 196608, 4063231, 393216, 16252927, 1572864, 65011711, 6291456, 260046847, 0, 956301311, 520093696, 3825205247, 2046820352, 14025752575, 6442450944 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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 = 181; 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]], 10], {i, 1, stages - 1}] CROSSREFS Cf. A286403, A286404, A286405. Sequence in context: A126612 A196113 A286506 * A070410 A077035 A076602 Adjacent sequences:  A286403 A286404 A286405 * A286407 A286408 A286409 KEYWORD nonn,easy AUTHOR Robert Price, May 08 2017 STATUS approved

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Last modified January 24 12:49 EST 2022. Contains 350538 sequences. (Running on oeis4.)