# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a288014 Showing 1-1 of 1 %I A288014 #7 Jun 04 2017 18:20:11 %S A288014 1,1,0,1,2,0,0,0,12,0,8,4,0,12,0,4,248,4,200,52,8,196,88,68,64,68,64, %T A288014 324,64,68,320,68,63552,324,63552,68,64,32836,1568,8580,0,4,98304, %U A288014 8676,0,1252,6144,49156,17376,131076,852064,32772,590624,1446084,426176 %N A288014 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 398", based on the 5-celled von Neumann neighborhood. %C A288014 Initialized with a single black (ON) cell at stage zero. %D A288014 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. %H A288014 Robert Price, Table of n, a(n) for n = 0..126 %H A288014 Robert Price, Diagrams of first 20 stages %H A288014 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 %H A288014 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A288014 S. Wolfram, A New Kind of Science %H A288014 Wolfram Research, Wolfram Atlas of Simple Programs %H A288014 Index entries for sequences related to cellular automata %H A288014 Index to 2D 5-Neighbor Cellular Automata %H A288014 Index to Elementary Cellular Automata %t A288014 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}]; %t A288014 code = 398; stages = 128; %t A288014 rule = IntegerDigits[code, 2, 10]; %t A288014 g = 2 * stages + 1; (* Maximum size of grid *) %t A288014 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *) %t A288014 ca = a; %t A288014 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}]; %t A288014 PrependTo[ca, a]; %t A288014 (* Trim full grid to reflect growth by one cell at each stage *) %t A288014 k = (Length[ca[[1]]] + 1)/2; %t A288014 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 A288014 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}] %Y A288014 Cf. A288012, A288013, A288015. %K A288014 nonn,easy %O A288014 0,5 %A A288014 _Robert Price_, Jun 04 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE