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 A282105 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 427", based on the 5-celled von Neumann neighborhood. 4
 1, 1, 7, 4, 29, 23, 124, 69, 471, 380, 1989, 1111, 7548, 6085, 31831, 17788, 120773, 97367, 509308, 284613, 1932375, 1557884, 8148933, 4553815, 30918012, 24926149, 130382935, 72861052, 494688197, 398818391, 2086126972, 1165776837, 7915011159, 6381094268 (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 FORMULA Empirical g.f.: (1 + x + 7*x^2 + 3*x^3 + 12*x^4 + 8*x^6 - 8*x^7) / ((1 - x)*(1 - 2*x)*(1 + 2*x)*(1 + x + x^2)*(1 + 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[1, i]], 2], {i, 1, stages - 1}] CROSSREFS Cf. A282103, A282104, A282106. Sequence in context: A281750 A282365 A281896 * A282259 A282453 A282654 Adjacent sequences:  A282102 A282103 A282104 * A282106 A282107 A282108 KEYWORD nonn,easy AUTHOR Robert Price, Feb 06 2017 STATUS approved

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Last modified August 10 11:52 EDT 2020. Contains 336379 sequences. (Running on oeis4.)