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 A270634 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 185", based on the 5-celled von Neumann neighborhood. 4
 1, 4, 9, 32, 33, 92, 65, 176, 53, 316, 113, 432, 189, 548, 284, 801, 300, 1028, 420, 1272, 476, 1488, 672, 1840, 676, 2180, 840, 2488, 976, 2828, 1212, 3320, 1260, 3716, 1424, 4272, 1448, 4656, 1780, 5256, 1932, 5700, 2212, 6284, 2432, 6740, 2816, 7564, 2828 (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 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=185; 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: A071378 A053192 A270618 * A324020 A265645 A005985 Adjacent sequences:  A270631 A270632 A270633 * A270635 A270636 A270637 KEYWORD nonn,easy AUTHOR Robert Price, Mar 20 2016 STATUS approved

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Last modified September 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)