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

1,17

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.

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.

Crossrefs

Cf. A271910, A272625, A272626.

Sequence in context: A316400 A061897 A047919 * A271223 A260944 A101670

Adjacent sequences: A272621 A272622 A272623 * A272625 A272626 A272627

Keyword

nonn,tabl

Author

Chai Wah Wu, May 07 2016

Status

approved