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 A151725 Number of ON states after n generations of cellular automaton based on square grid with each cell adjacent to its eight neighbors. 16
 0, 1, 9, 13, 33, 37, 57, 77, 121, 125, 145, 165, 209, 237, 297, 373, 465, 469, 489, 509, 553, 581, 641, 717, 809, 837, 897, 981, 1097, 1213, 1409, 1645, 1833, 1837, 1857, 1877, 1921, 1949, 2009, 2085, 2177, 2205, 2265, 2349, 2465, 2581, 2777, 3013 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A cell is turned ON if exactly one of its eight neighbors is ON. An ON cell remains ON forever. We start with a single ON cell. Analog of A147562, which is the case when each cell has only four neighbors. The equivalent Mathematica cellular automaton is obtained with neighborhood weights {{1,1,1},{1,9,1},{1,1,1}}, rule number 261634, and starting configuration {{1}}. [John W. Layman, Sep 11 2009] Observation: Visual pattern similar to the toothpick structure (see A139250). [Omar E. Pol, Dec 14 2009] LINKS David Applegate, Table of n, a(n) for n = 0..1000 David Applegate, The movie version David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.] N. H. Packard and S. Wolfram, Two-Dimensional Cellular Automata, Journal of Statistical Physics, 38 (1985), 901-946. (See page 920, Figure 7e). Alternative copy Rémy Sigrist, Illustration of the structure at stage 513 N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS FORMULA For a recurrence see the Applegate-Pol-Sloane paper. MATHEMATICA RasterGraphics[state_?MatrixQ, colors_Integer : 2, opts___] := Graphics[Raster[ Reverse[1 - state/(colors - 1)]], AspectRatio -> (AspectRatio /. {opts} /. AspectRatio -> Automatic), Frame -> True, FrameTicks -> None, GridLines -> None]; wt = {{1, 1, 1}, {1, 9, 1}, {1, 1, 1}}; rule= 261634; init={{1}}; Show[GraphicsArray[Map[RasterGraphics, CellularAutomaton[{rule, {2, wt}, {1, 1}}, {init, 0}, 9, -10]]]]; nx = 100; ca = CellularAutomaton[{rule, {2, wt}, {1, 1}}, {init, 0}, nx - 1, -nx]; a = Table[Total[ca[[i]], 2], {i, 1, nx}] (* John W. Layman, Sep 11 2009 *) A151725[0] = 0; A151725[n_] := Total[CellularAutomaton[{174766, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}}, {{{1}}, 0}, {{{n - 1}}}], 2]; Array[A151725, 48, 0] (* JungHwan Min, Sep 01 2016 *) A151725L[n_] := Prepend[Total[#, 2] & /@ CellularAutomaton[{174766, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}}, {{{1}}, 0}, n - 1], 0]; A151725L[47] (* JungHwan Min, Sep 01 2016 *) CROSSREFS Cf. A139250, A151726, A147562, A147582, A151723, A151735, A151747, A151728. See A151731, A151732, A151733, A151734 for the same CA except that two neighbors must be ON for a cell to turn ON. Sequence in context: A098074 A032361 A031196 * A146864 A287766 A146739 Adjacent sequences:  A151722 A151723 A151724 * A151726 A151727 A151728 KEYWORD nonn AUTHOR David Applegate and N. J. A. Sloane, Jun 13 2009 STATUS approved

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Last modified July 5 05:10 EDT 2022. Contains 355087 sequences. (Running on oeis4.)