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 A272581 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 505", based on the 5-celled von Neumann neighborhood. 4
 1, 4, 13, 40, 29, 100, 69, 200, 85, 324, 133, 480, 181, 644, 309, 872, 325, 1124, 373, 1408, 421, 1700, 565, 2048, 613, 2404, 757, 2792, 901, 3140, 1301, 3624, 1317, 4132, 1365, 4672, 1413, 5220, 1557, 5824, 1605, 6436, 1749, 7080, 1893, 7684, 2325, 8416 (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=505; 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: A133409 A000746 A271012 * A191132 A119915 A307577 Adjacent sequences:  A272578 A272579 A272580 * A272582 A272583 A272584 KEYWORD nonn,easy AUTHOR Robert Price, May 03 2016 STATUS approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)