A018811 Number of lines through exactly 4 points of an n X n grid of points.

0, 0, 0, 0, 10, 4, 4, 20, 44, 36, 64, 124, 200, 236, 272, 308, 548, 692, 852, 1108, 1396, 1452, 1768, 2116, 2496, 2908, 3568, 4292, 5428, 5956, 6500, 7444, 8452, 8980, 10208, 11516, 13348, 14700, 16116, 17596, 20124, 22476, 24956, 28092, 31404, 33052, 36032

Offset

0,5

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, 5) - 2 f(n, 4) + f(n, 3)) 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: A081986 A063566 A153690 * A309707 A100844 A076587

Adjacent sequences: A018808 A018809 A018810 * A018812 A018813 A018814

Keyword

nonn

Author

David W. Wilson

Status

approved