A018812 Number of lines through exactly 5 points of an n X n grid of points.

0, 0, 0, 0, 0, 12, 4, 4, 4, 24, 52, 40, 20, 76, 148, 236, 204, 228, 252, 356, 476, 612, 764, 932, 1116, 1524, 1548, 1556, 1548, 1884, 2252, 2652, 3084, 3820, 4620, 5484, 5524, 6140, 6788, 7468, 8180, 8588, 8996, 9932, 10916, 12868, 13820, 14804, 15820, 17668

Offset: 0

Author

David W. Wilson

Keywords

• nonn

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, 6) - 2 f(n, 5) + f(n, 4)) where f(n, k) = Sum ((n - |kx|)(n - |ky|)); -nSeppo Mustonen, Apr 18 2009]