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 A282577 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 553", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 1, 0, 5, 0, 21, 0, 85, 0, 341, 0, 1365, 0, 5461, 0, 21845, 0, 87381, 0, 349525, 0, 1398101, 0, 5592405, 0, 22369621, 0, 89478485, 0, 357913941, 0, 1431655765, 0, 5726623061, 0, 22906492245, 0, 91625968981, 0, 366503875925, 0, 1466015503701, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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 FORMULA Conjectures from Colin Barker, Feb 27 2017: (Start) a(n) = (2^n - 1) / 3 for n>1 and even. a(n) = 0 for n>1 and odd. a(n) = 5*a(n-2) - 4*a(n-4) for n>4. G.f.: (1 - 2*x^2)^2 / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)). (End) MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 553; 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. A282088, A282142, A282579. Sequence in context: A291926 A056461 A167355 * A279030 A176868 A279143 Adjacent sequences:  A282574 A282575 A282576 * A282578 A282579 A282580 KEYWORD nonn,easy AUTHOR Robert Price, Feb 27 2017 STATUS approved

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Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)