A018810 Number of lines through exactly 3 points of an n X n grid of points.

0, 0, 0, 8, 4, 16, 36, 64, 100, 204, 252, 396, 572, 780, 1020, 1484, 1756, 2260, 2828, 3540, 4332, 5556, 6372, 7716, 9188, 10684, 12292, 14684, 16588, 19324, 22268, 25420, 28780, 33164, 36452, 41036, 45892, 51324, 57060, 64540, 70500, 77724, 85300, 93228

Offset: 0

Author

David W. Wilson

Keywords

• nonn

References

• Lucien Pianaro, Jouer Jeux Mathematiques, 9(juillet 1993). [From Philippe Deléham, Apr 10 2009]

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• S. Mustonen, On lines and their intersection points in a rectangular grid of points [From _Seppo Mustonen_, Apr 18 2009]

Crossrefs

Cf. A119437.

Formula

a(n) = 1/2 (f(n, 4) - 2 f(n, 3) + f(n, 2)) where f(n, k) = Sum ((n - |kx|)(n - |ky|)); -nSeppo Mustonen, Apr 18 2009]