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A018809
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Number of lines through exactly 2 points of an n X n grid of points.
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5
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0, 0, 6, 12, 48, 108, 248, 428, 764, 1196, 1900, 2668, 3824, 5244, 7248, 9380, 12192, 15372, 19528, 24020, 29732, 36052, 43808, 51836, 61636, 72492, 85308, 98492, 114012, 130668, 150196, 170828, 194768, 220276, 249452, 279284, 312572, 348036
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (1/2) * (f(n, 3) - 2 f(n, 2) + f(n, 1)) where f(n, k) = Sum ((n - |kx|)(n - |ky|)); -n<kx<n, -n<ky<n, (x, y)=1. [Seppo Mustonen, Apr 18 2009]
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MATHEMATICA
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a[n_] := 1/2 (f[n, 3] - 2 f[n, 2] + f[n, 1]);
f[n_, k_] := Sum[x = kx/k; y = ky/k; If[IntegerQ[x] && IntegerQ[y] && CoprimeQ[x, y], (n - Abs[kx])(n - Abs[ky]), 0], {kx, -n + 1, n - 1}, {ky, -n + 1, n - 1}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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