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 A284027 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 782", based on the 5-celled von Neumann neighborhood. 4
 1, 3, 7, 11, 19, 55, 127, 235, 467, 759, 1471, 2667, 5267, 11383, 19711, 55531, 127187, 238071, 476863, 690283, 1118355, 3285111, 6291711, 8388843, 16777427, 50332151, 100665023, 134219883, 268439699, 805314679, 1610612991, 2147483883, 4294967507 (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 = 782; 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. A284024, A284025, A284026. Sequence in context: A355139 A191245 A282914 * A111056 A083908 A050577 Adjacent sequences: A284024 A284025 A284026 * A284028 A284029 A284030 KEYWORD nonn,easy AUTHOR Robert Price, Mar 18 2017 STATUS approved

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Last modified January 29 10:55 EST 2023. Contains 359922 sequences. (Running on oeis4.)