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 A272287 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 459", based on the 5-celled von Neumann neighborhood. 4
 1, 5, 9, 28, 25, 81, 32, 145, 101, 244, 57, 421, 156, 537, 153, 656, 309, 893, 185, 1149, 389, 1372, 345, 1556, 613, 1909, 460, 2237, 669, 2468, 721, 2745, 1120, 3341, 961, 3836, 965, 4213, 1104, 4665, 1337, 5096, 1237, 5653, 1500, 6025, 1524, 6489, 2136 (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=459; 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: A222357 A271685 A271807 * A272315 A301747 A193316 Adjacent sequences: A272284 A272285 A272286 * A272288 A272289 A272290 KEYWORD nonn,easy,changed AUTHOR Robert Price, Apr 24 2016 STATUS approved

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Last modified August 9 18:14 EDT 2024. Contains 375044 sequences. (Running on oeis4.)