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

0,6

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, 6) - 2 f(n, 5) + f(n, 4)) 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: A010202 A079792 A079791 * A306375 A139358 A004477

Adjacent sequences: A018809 A018810 A018811 * A018813 A018814 A018815

Keyword

nonn

Author

David W. Wilson

Status

approved