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 A278424 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 41", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 4, 3, 20, 3, 112, 47, 272, 143, 1088, 575, 4416, 2111, 22272, 2815, 114944, 47359, 283648, 132095, 1168384, 558079, 4485120, 2273279, 22024192, 757759, 130367488, 44056575, 274546688, 237518847, 1158086656, 552271871, 4785766400, 2822307839 (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 MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=41; 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. A278421, A278422, A278423. Sequence in context: A178417 A178628 A167479 * A278662 A220861 A270797 Adjacent sequences:  A278421 A278422 A278423 * A278425 A278426 A278427 KEYWORD nonn,easy AUTHOR Robert Price, Nov 21 2016 STATUS approved

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Last modified November 30 02:42 EST 2020. Contains 338781 sequences. (Running on oeis4.)