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.

%I A272625 #7 May 10 2016 09:12:38
%S A272625 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,
%T A272625 84,84,44,0,0,0,0,60,128,164,128,60,0,0,0,0,78,176,264,264,176,78,0,0,
%U A272625 0,0,98,228,374,448,374,228,98,0,0,0,0,120,284,492,650
%N 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.
%C A272625 A271910(n) = A272624(n) + a(n) + A272626(n).
%H A272625 Chai Wah Wu, <a href="/A272625/b272625.txt">Table of n, a(n) for n = 1..3003</a>
%H A272625 Chai Wah Wu, <a href="http://arxiv.org/abs/1605.00180">Counting the number of isosceles triangles in rectangular regular grids</a>, arXiv:1605.00180 [math.CO], 2016.
%F A272625 T(n,k) = 3*T(n,k-1)-3*T(n,k-2)+T(n,k-3) for k > (n-1)^2+1.
%Y A272625 Cf. A271910, A272624, A272626.
%K A272625 nonn,tabl
%O A272625 1,13
%A A272625 _Chai Wah Wu_, May 07 2016