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 A281212 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 334", based on the 5-celled von Neumann neighborhood. 4
 1, 3, 6, 15, 24, 60, 98, 247, 400, 1016, 1540, 3850, 6547, 16382, 24577, 61443, 104454, 261131, 393748, 984358, 1673471, 4183296, 6292352, 15729856, 26742624, 66853136, 100804520, 252008524, 428688626, 1071148943, 1610913872, 4027278584, 6846831492 (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 = 334; 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. A280099, A280165, A281213. Sequence in context: A118035 A272073 A282008 * A062878 A282387 A227960 Adjacent sequences:  A281209 A281210 A281211 * A281213 A281214 A281215 KEYWORD nonn,easy AUTHOR Robert Price, Jan 17 2017 STATUS approved

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Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)