A165345 Number of ON cells after n generations of the 2D cellular automaton described in the comments.

1, 5, 9, 25, 29, 41, 53, 105, 113, 129, 141, 193, 205, 241, 285, 433, 453, 481, 497, 553, 569, 609, 653, 801, 829, 881, 917, 1073, 1109, 1217, 1349, 1793, 1845, 1905, 1933, 2001, 2029, 2081, 2129, 2281, 2313, 2369, 2409, 2569, 2609, 2721, 2853, 3297, 3357

Offset: 1

Author

John W. Layman, Sep 15 2009, Sep 16 2009

Keywords

• nonn

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) it was ON, or (2) exactly one of the four nearest side neighbors was ON, or (3) exactly three of the four nearest corner neighbors were ON, in the previous generation

The equivalent Mathematica automaton is obtained with neighborhood weights {{10,2,10},{2,1,2},{10,2,10}}, rule number 755364134566574, and initial configuration {{1}} (see code).

Links

• Graphs of the automaton for generations 1-20. [From _John W. Layman_, Sep 15 2009]

Crossrefs

Cf. A048883, A072272, A122108, A160410, A164982.

Programs

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 = {{10, 2, 10}, {2, 1, 2}, {10, 2, 10}}; rule=755364134566574; init = {{1}}; Show[GraphicsArray[ Map[RasterGraphics, CellularAutomaton[{rule, {2, wt}, {1, 1}}, {init, 0}, 9, -10]]]]; ca = CellularAutomaton[{rule, {2, wt}, {1, 1}}, {init, 0}, 99, -100]; a = Table[Total[ca[[i]], 2], {i, 1, 100}]