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 A279139 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 133", based on the 5-celled von Neumann neighborhood. 4
 1, 2, 2, 12, 7, 60, 3, 246, 16, 995, 36, 4043, 112, 16347, 80, 65419, 208, 262027, 64, 1048227, 540, 4193303, 1540, 16776635, 426, 67106688, 5231, 268427872, 9519, 1073731776, 4079, 4294922240, 67567, 17179777024, 163247, 68719263872, 343311, 274877424848 (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 = 133; 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. A279137, A279138, A279140. Sequence in context: A256120 A024538 A279879 * A279754 A279147 A279824 Adjacent sequences:  A279136 A279137 A279138 * A279140 A279141 A279142 KEYWORD nonn,easy AUTHOR Robert Price, Dec 06 2016 STATUS approved

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Last modified August 9 01:03 EDT 2020. Contains 336309 sequences. (Running on oeis4.)