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 A279700 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 185", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 5, 0, 23, 4, 85, 20, 321, 92, 1365, 328, 5195, 1346, 21592, 5467, 83294, 21854, 345430, 87382, 1328470, 349526, 5522774, 1398102, 21316950, 5592406, 88425814, 22369622, 340084054, 89478486, 1413825878, 357913942, 5457134934, 1431655766, 22637004118 (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 Index entries for sequences related to cellular automata Index to 2D 5-Neighbor Cellular Automata Index to Elementary Cellular Automata FORMULA Conjectures from Chai Wah Wu, May 04 2024: (Start) a(n) = a(n-2) + 256*a(n-8) - 256*a(n-10) for n > 27. G.f.: (2048*x^27 + 2048*x^26 - 768*x^25 - 1536*x^24 - 6400*x^23 - 3328*x^22 + 1536*x^21 + 2560*x^20 + 5112*x^19 - 5128*x^18 - 2045*x^17 + 1286*x^16 + 25*x^15 + 525*x^14 - 6*x^13 - 778*x^12 + 236*x^11 + 20*x^10 + 72*x^9 - 20*x^8 + 16*x^7 + 62*x^6 + 4*x^5 + 18*x^4 + 4*x^2 + 1)/(256*x^10 - 256*x^8 - x^2 + 1). (End) MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 185; 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. A279698, A279699, A279701. Sequence in context: A279500 A185246 A279547 * A279603 A329252 A022665 Adjacent sequences: A279697 A279698 A279699 * A279701 A279702 A279703 KEYWORD nonn,easy AUTHOR Robert Price, Dec 17 2016 STATUS approved

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Last modified September 13 22:05 EDT 2024. Contains 375910 sequences. (Running on oeis4.)