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 A278469 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 49", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 4, 3, 16, 15, 64, 63, 288, 31, 1920, 127, 7680, 2559, 16384, 16383, 75264, 511, 522240, 206847, 1048576, 1048575, 5070848, 73727, 33193984, 3047423, 120061952, 5767167, 511115264, 139526143, 1179385856, 537133055, 5904531456, 1255145471, 25769803776 (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=49; 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. A278466, A278467, A278468. Sequence in context: A285122 A277773 A277800 * A280976 A285646 A092398 Adjacent sequences: A278466 A278467 A278468 * A278470 A278471 A278472 KEYWORD nonn,easy AUTHOR Robert Price, Nov 22 2016 STATUS approved

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Last modified March 22 20:34 EDT 2023. Contains 361433 sequences. (Running on oeis4.)