A272626 Array read by antidiagonals: T(n,k) = number of ways to choose 3 distinct points from an n X k rectangular grid so that they form a right isosceles triangle of nonzero area.

0, 0, 0, 0, 4, 0, 0, 10, 10, 0, 0, 16, 28, 16, 0, 0, 22, 50, 50, 22, 0, 0, 28, 74, 96, 74, 28, 0, 0, 34, 98, 150, 150, 98, 34, 0, 0, 40, 122, 208, 244, 208, 122, 40, 0, 0, 46, 146, 268, 350, 350, 268, 146, 46, 0, 0, 52, 170, 328, 464, 516, 464, 328, 170, 52, 0

Offset

1,5

Comments

A271910(n) = A272624(n) + A272625(n) + a(n).

Links

Chai Wah Wu, Table of n, a(n) for n = 1..3003

Chai Wah Wu, Counting the number of isosceles triangles in rectangular regular grids, arXiv:1605.00180 [math.CO], 2016.

Formula

T(n,k) = 2*T(n,k-1)-T(n,k-2) for k > max(5,(n-1)^2).

Crossrefs

Cf. A271910, A272624, A272625.

Sequence in context: A244121 A127774 A127319 * A271910 A249346 A035539

Adjacent sequences: A272623 A272624 A272625 * A272627 A272628 A272629

Keyword

nonn,tabl

Author

Chai Wah Wu, May 07 2016

Status

approved