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A350632
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a(n) is the total number of ON cells at stage n of a cellular automaton where cells are turned ON when they have one or two neighbors ON (see Comments for precise definition).
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4
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0, 1, 9, 21, 45, 57, 85, 121, 177, 189, 217, 253, 329, 373, 465, 557, 721, 737, 765, 801, 877, 921, 1013, 1105, 1301, 1377, 1485, 1601, 1805, 1985, 2221, 2449, 2873, 2909, 2937, 2973, 3049, 3093, 3185, 3277, 3473, 3549, 3657, 3773, 3977, 4157, 4393, 4621, 5113
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OFFSET
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0,3
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COMMENTS
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On the infinite square grid, start with all cells OFF.
Turn a single cell to the ON state.
At each subsequent step, each cell with exactly one or two neighbors ON is turned ON, and everything that is already ON remains ON.
Here "neighbor" refers to the eight adjacent and diagonally adjacent cells in the Moore neighborhood.
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LINKS
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EXAMPLE
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The first 5 generations can be depicted as follows:
. . . . . . . . . . .
. 5 5 . . . . . 5 5 .
. 5 4 4 4 4 4 4 4 5 .
. . 4 3 3 . 3 3 4 . .
. . 4 3 2 2 2 3 4 . .
. . 4 . 2 1 2 . 4 . .
. . 4 3 2 2 2 3 4 . .
. . 4 3 3 . 3 3 4 . .
. 5 4 4 4 4 4 4 4 5 .
. 5 5 . . . . . 5 5 .
. . . . . . . . . . .
- so a(0) = 0,
a(1) = 0 + 1 = 1,
a(2) = 1 + 8 = 9,
a(3) = 9 + 12 = 21,
a(4) = 21 + 24 = 45,
a(5) = 45 + 12 = 57.
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PROG
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(C++) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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