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A178256
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Number of ways to choose four collinear points from an n X n grid.
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6
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0, 0, 0, 10, 64, 234, 660, 1524, 3156, 5928, 10428, 17154, 27340, 41506, 61176, 87756, 123216, 168420, 227208, 300054, 391920, 504886, 642604, 806424, 1006404, 1242024, 1519980, 1845150, 2226804, 2663574, 3175048, 3754936, 4420440, 5175840, 6030840
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OFFSET
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1,4
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LINKS
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EXAMPLE
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a(1) = a(2) = a(3) = 0 since there are no collinear point quadruples
a(4) = 4 rows + 4 columns + 2 diagonals = 10
a(5) = binomial(5,4)*(5 rows + 5 columns + 2 diagonals) + 4 secondary diagonals = 64
a(6) = binomial(6,4)*(6 rows + 6 columns + 2 diagonals) + binomial(5,4)*(4 secondary diagonals) + 4 third diagonals = 234
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CROSSREFS
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This is the main diagonal of A334708.
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010
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STATUS
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approved
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