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 A290855 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 998", based on the 5-celled von Neumann neighborhood. 4
 1, 2, 4, 8, 16, 32, 64, 128, 352, 704, 1408, 2816, 5888, 11776, 23552, 47104, 94208, 192512, 385024, 782336, 1564672, 3129344, 6258688, 12550144, 25116672, 50233344, 100597760, 201261056, 402587648, 805175296, 1610350592, 3220701184, 6442319872, 12884639744 (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 = 998; 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 Diagrams of first 20 stages Cf. A290852, A290853, A290854. Sequence in context: A290625 A275074 A290687 * A264791 A290851 A290670 Adjacent sequences:  A290852 A290853 A290854 * A290856 A290857 A290858 KEYWORD nonn,easy AUTHOR Robert Price, Aug 12 2017 STATUS approved

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Last modified January 17 06:12 EST 2022. Contains 350378 sequences. (Running on oeis4.)