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 A274473 Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 22", based on the 5-celled von Neumann neighborhood. 4
 1, 3, 1, 3, 1, 3, 17, 51, 1, 3, 17, 51, 257, 771, 4369, 13107, 1, 3, 17, 51, 257, 771, 4369, 13107, 65537, 196611, 1114129, 3342387, 16843009, 50529027, 286331153, 858993459, 1, 3, 17, 51, 257, 771, 4369, 13107, 65537, 196611, 1114129, 3342387, 16843009 (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 Index entries for sequences related to cellular automata Index to 2D 5-Neighbor Cellular Automata Index to Elementary Cellular Automata MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=22; 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[i, 2*i-1]], 2], {i, 1, stages-1}] CROSSREFS Cf. A274060, A274216, A274224. Sequence in context: A023892 A085417 A201662 * A280526 A335552 A306841 Adjacent sequences: A274470 A274471 A274472 * A274474 A274475 A274476 KEYWORD nonn,easy AUTHOR Robert Price, Nov 10 2016 STATUS approved

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Last modified May 30 13:54 EDT 2023. Contains 363050 sequences. (Running on oeis4.)