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

1,2

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) 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

Table of n, a(n) for n=1..49.

Graphs of the automaton for generations 1-20. [From John W. Layman, Sep 15 2009]

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}]

Crossrefs

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

Sequence in context: A146419 A365070 A162907 * A177240 A074741 A166701

Adjacent sequences: A165342 A165343 A165344 * A165346 A165347 A165348

Keyword

nonn

Author

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

Status

approved