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A164982
Number of ON cells after n generations of the 2D cellular automaton described in the comments.
4
1, 3, 4, 12, 7, 21, 16, 40, 22, 42, 34, 67, 52, 85, 70, 125, 94, 126, 102, 150, 118, 172, 177, 234, 209, 240, 238, 319, 285, 363, 378, 458, 383, 444, 404, 493, 474, 520, 529, 628, 583, 602, 622, 727, 664, 816, 835, 948, 873, 926, 952, 1065, 1010, 1090, 1187
OFFSET
1,2
COMMENTS
The cells are the squares of the standard square grid. All cells are initially OFF and one cell is turned ON at generation 1. At subsequent generations a cell is ON if and only if (1) exactly one of neighbors NW, NE, and S was ON, or (2) all three of cells N, SW, and SE were ON in the previous generation. (The 9-cell Moore neighborhood is labeled {{NW,N,NE},{W,C,E},{SW,S,SE}}).
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];
rule=61986;
Show[GraphicsArray[Map[RasterGraphics, CellularAutomaton[{rule, {2, {{1, 4, 1}, {0, 0, 0}, {4, 1, 4}}}, {1, 1}}, {{{1}}, 0}, 4, -5]]]];
ca = CellularAutomaton[{rule, {2, {{1, 4, 1}, {0, 0, 0}, {4, 1, 4}}}, {1, 1}}, {{{1}}, 0}, 99, -100];
Table[Total[ca[[i]], 2], {i, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Sep 03 2009
STATUS
approved