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%I #21 Oct 30 2018 03:30:39
%S 0,0,6,12,48,108,248,428,764,1196,1900,2668,3824,5244,7248,9380,12192,
%T 15372,19528,24020,29732,36052,43808,51836,61636,72492,85308,98492,
%U 114012,130668,150196,170828,194768,220276,249452,279284,312572,348036
%N Number of lines through exactly 2 points of an n X n grid of points.
%H Seiichi Manyama, <a href="/A018809/b018809.txt">Table of n, a(n) for n = 0..1000</a>
%H S. Mustonen, <a href="http://www.survo.fi/papers/PointsInGrid.pdf">On lines and their intersection points in a rectangular grid of points</a> [From _Seppo Mustonen_, Apr 18 2009]
%F 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]
%t a[n_] := 1/2 (f[n, 3] - 2 f[n, 2] + f[n, 1]);
%t 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}];
%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Oct 30 2018 *)
%K nonn
%O 0,3
%A _David W. Wilson_
%E An incorrect formula removed by _Seppo Mustonen_, Apr 25 2009
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