

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.


3



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
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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,k1)2*T(n,k3)+T(n,k4) for k > max(7,(n1)^2+2) if n is odd and for k > (n1)^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



