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

0,4

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]

Formula

a(n) = 1/2 (f(n, 4) - 2 f(n, 3) + f(n, 2)) where f(n, k) = Sum ((n - |kx|)(n - |ky|)); -n<kx<n, -n<ky<n, (x, y)=1. [From Seppo Mustonen, Apr 18 2009]

Crossrefs

Cf. A119437.

Sequence in context: A276071 A040059 A178603 * A070485 A248293 A151726

Adjacent sequences: A018807 A018808 A018809 * A018811 A018812 A018813

Keyword

nonn

Author

David W. Wilson

Status

approved