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 A282106 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 427", based on the 5-celled von Neumann neighborhood. 4
 1, 2, 7, 2, 23, 58, 31, 162, 471, 250, 1311, 3746, 2007, 10490, 29983, 16034, 83927, 239866, 128287, 671394, 1918935, 1026298, 5371167, 15351458, 8210391, 42969338, 122811679, 65683106, 343754711, 982493434, 525464863, 2750037666, 7859947479, 4203718906 (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 FORMULA Empirical g.f.: (1 + 2*x + 7*x^2 - 6*x^3 + 6*x^4 + 8*x^6 - 16*x^7) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + x^2)*(1 + 2*x + 4*x^2)). - Colin Barker, Feb 06 2017 MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 427; 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. A282103, A282104, A282105. Sequence in context: A281751 A282366 A281897 * A282260 A217202 A100489 Adjacent sequences:  A282103 A282104 A282105 * A282107 A282108 A282109 KEYWORD nonn,easy AUTHOR Robert Price, Feb 06 2017 STATUS approved

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Last modified September 20 23:04 EDT 2021. Contains 347596 sequences. (Running on oeis4.)