A272625 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 an acute isosceles triangle of nonzero area.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 18, 18, 0, 0, 0, 0, 30, 48, 30, 0, 0, 0, 0, 44, 84, 84, 44, 0, 0, 0, 0, 60, 128, 164, 128, 60, 0, 0, 0, 0, 78, 176, 264, 264, 176, 78, 0, 0, 0, 0, 98, 228, 374, 448, 374, 228, 98, 0, 0, 0, 0, 120, 284, 492, 650

Offset

1,13

Comments

A271910(n) = A272624(n) + a(n) + A272626(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) = 3*T(n,k-1)-3*T(n,k-2)+T(n,k-3) for k > (n-1)^2+1.

Crossrefs

Cf. A271910, A272624, A272626.

Sequence in context: A079204 A374087 A325737 * A334709 A220667 A317445

Adjacent sequences: A272622 A272623 A272624 * A272626 A272627 A272628

Keyword

nonn,tabl

Author

Chai Wah Wu, May 07 2016

Status

approved