# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a286700 Showing 1-1 of 1 %I A286700 #7 May 12 2017 23:15:23 %S A286700 1,2,1,14,1,60,3,252,3,1008,15,4080,15,16368,15,65520,15,261888,255, %T A286700 1048320,255,4194048,239,16776976,239,67108352,511,268434944,123, %U A286700 1073740676,1083,4294966212,1083,17179810180,58979,68719411612,65027,274877841916,65027 %N A286700 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 209", based on the 5-celled von Neumann neighborhood. %C A286700 Initialized with a single black (ON) cell at stage zero. %D A286700 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. %H A286700 Robert Price, Table of n, a(n) for n = 0..126 %H A286700 Robert Price, Diagrams of first 20 stages %H A286700 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 %H A286700 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A286700 S. Wolfram, A New Kind of Science %H A286700 Wolfram Research, Wolfram Atlas of Simple Programs %H A286700 Index entries for sequences related to cellular automata %H A286700 Index to 2D 5-Neighbor Cellular Automata %H A286700 Index to Elementary Cellular Automata %t A286700 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}]; %t A286700 code = 209; stages = 128; %t A286700 rule = IntegerDigits[code, 2, 10]; %t A286700 g = 2 * stages + 1; (* Maximum size of grid *) %t A286700 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *) %t A286700 ca = a; %t A286700 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}]; %t A286700 PrependTo[ca, a]; %t A286700 (* Trim full grid to reflect growth by one cell at each stage *) %t A286700 k = (Length[ca[[1]]] + 1)/2; %t A286700 ca = Table[Table[Part[ca[[n]] [[j]],Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}]; %t A286700 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}] %Y A286700 Cf. A286698, A286699, A286701. %K A286700 nonn,easy %O A286700 0,2 %A A286700 _Robert Price_, May 12 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE