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 A271685 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 395", based on the 5-celled von Neumann neighborhood. 4
 1, 5, 9, 28, 17, 89, 32, 145, 53, 268, 77, 377, 100, 533, 213, 624, 161, 921, 208, 1101, 253, 1380, 361, 1509, 404, 1865, 453, 2124, 513, 2453, 720, 2625, 669, 3172, 749, 3593, 756, 4149, 937, 4452, 1009, 4953, 1248, 5273, 1317, 5912, 1525, 6185, 1524, 6929 (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=395; 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: A374025 A077915 A222357 * A271807 A272287 A272315 Adjacent sequences: A271682 A271683 A271684 * A271686 A271687 A271688 KEYWORD nonn,easy AUTHOR Robert Price, Apr 12 2016 STATUS approved

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Last modified August 10 19:25 EDT 2024. Contains 375058 sequences. (Running on oeis4.)