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 A287628 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 318", based on the 5-celled von Neumann neighborhood. 4
 1, 1, 2, 3, 7, 4, 12, 15, 30, 30, 62, 34, 98, 94, 230, 150, 414, 382, 846, 734, 1902, 1278, 3214, 2959, 8062, 4442, 12714, 10842, 32166, 17262, 50334, 42726, 125718, 73406, 205758, 176766, 513722, 278378, 809386, 686442, 2000794, 1164410, 3296442, 2847482 (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 MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 318; 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[i, 2 * i - 1]], 10], {i, 1, stages - 1}] CROSSREFS Cf. A287626, A287627, A287629. Sequence in context: A168087 A168085 A287950 * A319863 A320948 A086885 Adjacent sequences:  A287625 A287626 A287627 * A287629 A287630 A287631 KEYWORD nonn,easy AUTHOR Robert Price, May 28 2017 STATUS approved

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Last modified August 12 23:52 EDT 2022. Contains 356077 sequences. (Running on oeis4.)