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 A278759 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 73", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 3, 10, 0, 63, 0, 255, 0, 1023, 0, 4095, 0, 16383, 0, 65535, 0, 262143, 0, 1048575, 0, 4194303, 0, 16777215, 0, 67108863, 0, 268435455, 0, 1073741823, 0, 4294967295, 0, 17179869183, 0, 68719476735, 0, 274877906943, 0, 1099511627775, 0, 4398046511103, 0 (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 FORMULA Conjectures from Chai Wah Wu, Jun 14 2020: (Start) a(n) = 5*a(n-2) - 4*a(n-4) for n > 7. G.f.: (-20*x^7 + 12*x^6 + 13*x^5 - 11*x^4 + 10*x^3 - 2*x^2 + 1)/(4*x^4 - 5*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=73; 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. A278757, A278758, A278760. Sequence in context: A336747 A212361 A011998 * A280752 A182303 A165590 Adjacent sequences:  A278756 A278757 A278758 * A278760 A278761 A278762 KEYWORD nonn,easy AUTHOR Robert Price, Nov 27 2016 STATUS approved

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)