A272624 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 obtuse isosceles triangle of nonzero area.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 4, 4, 4, 4, 0, 0, 8, 8, 14, 14, 8, 8, 0, 0, 12, 18, 24, 36, 24, 18, 12, 0, 0, 18, 28, 44, 58, 58, 44, 28, 18, 0, 0, 24, 44, 64, 94, 100, 94, 64, 44, 24, 0, 0, 32, 60, 96, 130, 160, 160, 130, 96

Offset: 1

Author

Chai Wah Wu, May 07 2016

Keywords

• nonn
• tabl

Comments

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

Crossrefs

Cf. A271910, A272625, A272626.

Formula

T(n,k) = 2*T(n,k-1)-2*T(n,k-3)+T(n,k-4) for k > max(7,(n-1)^2+2) if n is odd and for k > (n-1)^2+3) if n is even.