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A234251
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Triangle T(n, k) = Number of ways to choose k points from an n X n X n triangular grid so that no three of them form a 2 X 2 X 2 subtriangle. Triangle T read by rows.
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4
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1, 1, 1, 3, 3, 1, 6, 15, 16, 6, 1, 10, 45, 111, 156, 120, 42, 2, 1, 15, 105, 439, 1191, 2154, 2583, 1977, 885, 189, 9, 1, 21, 210, 1305, 5565, 17052, 38337, 63576, 77208, 67285, 40512, 15750, 3480, 333, 9, 1, 28, 378, 3240, 19620, 88590, 307362, 833228, 1779219
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OFFSET
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1,4
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COMMENTS
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n starts from 1. The maximal number of points that can be chosen from a grid of side n, so that no three of them are forming a subtriangle of side 2, is A007980(n - 1). So k ranges from 0 to A007980(n - 1).
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LINKS
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EXAMPLE
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Triangle begins
1, 1;
1, 3, 3;
1, 6, 15, 16, 6;
1, 10, 45, 111, 156, 120, 42, 2;
1, 15, 105, 439, 1191, 2154, 2583, 1977, 885, 189, 9;
...
There are no more than T(4, 7) = 2 ways to choose 7 points (X) from a 4 X 4 X 4 grid so that no 3 of them form a 2 X 2 X 2 subtriangle:
X X
X . . X
. X X X X .
X X . X X . X X
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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