A272624 -id:A272624 - cp's OEIS frontend

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

Chai Wah Wu, May 07 2016

A271910(n) = A272624(n) + a(n) + A272626(n).

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.

Cf. A271910, A272624, A272626.

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

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.

Original entry on oeis.org

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

Chai Wah Wu, May 07 2016

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

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.

Cf. A271910, A272624, A272625.

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

cp's OEIS Frontend

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.

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