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 A272705 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 515", based on the 5-celled von Neumann neighborhood. 4
 1, 5, 13, 25, 49, 69, 109, 137, 193, 229, 301, 345, 433, 485, 589, 649, 769, 837, 973, 1049, 1201, 1285, 1453, 1545, 1729, 1829, 2029, 2137, 2353, 2469, 2701, 2825, 3073, 3205, 3469, 3609, 3889, 4037, 4333, 4489, 4801, 4965, 5293, 5465, 5809, 5989, 6349 (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..128 Robert Price, Diagrams of the 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=515; 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}]; Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *) CROSSREFS Sequence in context: A147166 A146192 A147265 * A147272 A147427 A147408 Adjacent sequences: A272702 A272703 A272704 * A272706 A272707 A272708 KEYWORD nonn,easy AUTHOR Robert Price, May 04 2016 STATUS approved

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Last modified February 20 16:34 EST 2024. Contains 370213 sequences. (Running on oeis4.)