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 A270725 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 203", based on the 5-celled von Neumann neighborhood. 4
 1, 5, 5, 33, 13, 93, 33, 177, 29, 301, 53, 437, 73, 593, 157, 777, 129, 1025, 165, 1289, 209, 1601, 209, 1873, 277, 2221, 341, 2537, 429, 2897, 613, 3209, 649, 3693, 741, 4217, 821, 4825, 749, 5365, 801, 5993, 773, 6617, 805, 7149, 1097, 7721, 1033, 8393 (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=203; 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: A270221 A270689 A270278 * A317812 A298961 A298721 Adjacent sequences: A270722 A270723 A270724 * A270726 A270727 A270728 KEYWORD nonn,easy,changed AUTHOR Robert Price, Mar 22 2016 STATUS approved

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Last modified August 5 21:25 EDT 2024. Contains 374956 sequences. (Running on oeis4.)