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 A280614 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 297", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 1, 12, 5, 50, 1, 244, 17, 964, 17, 4036, 85, 16170, 17, 65348, 277, 261194, 257, 1047676, 1281, 4190844, 69, 16774930, 5201, 67094820, 1, 268427228, 20561, 1073686308, 1, 4294932340, 87377, 17179650724, 21761, 68719291004, 267333, 274876975378, 344385 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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 = 297; 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. A280612, A280613, A280615. Sequence in context: A299516 A278423 A278661 * A281041 A038331 A028578 Adjacent sequences: A280611 A280612 A280613 * A280615 A280616 A280617 KEYWORD nonn,easy AUTHOR Robert Price, Jan 06 2017 STATUS approved

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Last modified March 30 00:49 EDT 2023. Contains 361599 sequences. (Running on oeis4.)