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 A272007 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 413", based on the 5-celled von Neumann neighborhood. 3
 1, 8, 5, 48, 5, 120, 5, 224, 5, 360, 5, 528, 5, 728, 5, 960, 5, 1224, 5, 1520, 5, 1848, 5, 2208, 5, 2600, 5, 3024, 5, 3480, 5, 3968, 5, 4488, 5, 5040, 5, 5624, 5, 6240, 5, 6888, 5, 7568, 5, 8280, 5, 9024, 5, 9800, 5, 10608, 5, 11448, 5, 12320, 5, 13224, 5 (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 MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=413; 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: A272111 A272291 A272543 * A296437 A038283 A317402 Adjacent sequences:  A272004 A272005 A272006 * A272008 A272009 A272010 KEYWORD nonn,easy AUTHOR Robert Price, Apr 17 2016 STATUS approved

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Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)