A178256 Number of ways to choose four collinear points from an n X n grid.

0, 0, 0, 10, 64, 234, 660, 1524, 3156, 5928, 10428, 17154, 27340, 41506, 61176, 87756, 123216, 168420, 227208, 300054, 391920, 504886, 642604, 806424, 1006404, 1242024, 1519980, 1845150, 2226804, 2663574, 3175048, 3754936, 4420440, 5175840, 6030840

Offset

1,4

Links

Tomas Rokicki and Tom Duff, Table of n, a(n) for n = 1..1000 (First 48 terms from R. H. Hardin.)

Example

a(1) = a(2) = a(3) = 0 since there are no collinear point quadruples
a(4) = 4 rows + 4 columns + 2 diagonals = 10
a(5) = binomial(5,4)*(5 rows + 5 columns + 2 diagonals) + 4 secondary diagonals = 64
a(6) = binomial(6,4)*(6 rows + 6 columns + 2 diagonals) + binomial(5,4)*(4 secondary diagonals) + 4 third diagonals = 234

Crossrefs

Cf. A000938, A157882.

This is the main diagonal of A334708.

Sequence in context: A138661 A341681 A269538 * A036426 A245068 A055855

Adjacent sequences: A178253 A178254 A178255 * A178257 A178258 A178259

Keyword

nonn

Author

R. H. Hardin, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010

Status

approved