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 A280835 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 299", based on the 5-celled von Neumann neighborhood. 4
 1, 1, 3, 8, 1, 61, 7, 240, 23, 988, 49, 3973, 23, 16344, 99, 65288, 329, 261577, 777, 1046601, 329, 4193737, 1545, 16773321, 5193, 67099977, 13257, 268402761, 5449, 1073733577, 24905, 4294905289, 83721, 17179727177, 212937, 68718952457, 90057, 274877771849 (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 = 299; 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[1, i]], 2], {i, 1, stages - 1}] CROSSREFS Cf. A280833, A280834, A280836. Sequence in context: A281306 A281416 A280567 * A195426 A202537 A220516 Adjacent sequences:  A280832 A280833 A280834 * A280836 A280837 A280838 KEYWORD nonn,easy AUTHOR Robert Price, Jan 08 2017 STATUS approved

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Last modified June 4 01:05 EDT 2020. Contains 334808 sequences. (Running on oeis4.)