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 A272330 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 601", based on the 5-celled von Neumann neighborhood. 4
 1, 4, 17, 29, 61, 73, 132, 148, 244, 224, 357, 349, 505, 461, 705, 645, 956, 816, 1144, 996, 1413, 1205, 1749, 1477, 2057, 1717, 2389, 2097, 2764, 2364, 3225, 2781, 3669, 3029, 4116, 3408, 4605, 3833, 5129, 4329, 5717, 4725, 6257, 5241, 6792, 5708, 7529 (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 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 Robert Price, Diagrams of the first 20 stages MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=601; 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: A272991 A273430 A273073 * A163736 A249582 A127547 Adjacent sequences: A272327 A272328 A272329 * A272331 A272332 A272333 KEYWORD nonn,easy AUTHOR Robert Price, May 17 2016 STATUS approved

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Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)