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 A281892 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 406", based on the 5-celled von Neumann neighborhood. 4
 1, 3, 4, 12, 20, 62, 65, 201, 337, 1019, 1028, 3204, 5396, 16188, 16388, 51750, 87041, 261633, 262149, 821927, 1377604, 4130788, 4214784, 13301920, 22348864, 67054696, 67114064, 210255602, 352403729, 1057734939, 1078203412, 3404086844, 5721096192 (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 = 406; 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. A281095, A281096, A281893. Sequence in context: A279248 A026553 A282220 * A101727 A292551 A227429 Adjacent sequences:  A281889 A281890 A281891 * A281893 A281894 A281895 KEYWORD nonn,easy AUTHOR Robert Price, Feb 01 2017 STATUS approved

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Last modified September 19 04:50 EDT 2020. Contains 337175 sequences. (Running on oeis4.)