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 A288338 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 446", based on the 5-celled von Neumann neighborhood. 4
 1, 1, 2, 3, 4, 6, 10, 13, 18, 29, 46, 57, 78, 109, 178, 205, 306, 461, 754, 909, 1266, 1741, 2866, 3789, 4914, 6861, 12082, 14541, 19442, 28173, 45554, 52749, 81266, 115533, 195762, 230221, 326834, 443213, 736434, 967501, 1260722, 1753933, 3095730, 3720013 (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 = 446; 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. A288336, A288337, A288339. Sequence in context: A273542 A061018 A130126 * A121152 A229863 A215255 Adjacent sequences:  A288335 A288336 A288337 * A288339 A288340 A288341 KEYWORD nonn,easy AUTHOR Robert Price, Jun 07 2017 STATUS approved

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Last modified July 31 19:01 EDT 2021. Contains 346376 sequences. (Running on oeis4.)