cp's OEIS Frontend

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.

%I A272626 #10 May 10 2016 09:12:46
%S A272626 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,
%T A272626 0,0,34,98,150,150,98,34,0,0,40,122,208,244,208,122,40,0,0,46,146,268,
%U A272626 350,350,268,146,46,0,0,52,170,328,464,516,464,328,170,52,0
%N 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.
%C A272626 A271910(n) = A272624(n) + A272625(n) + a(n).
%H A272626 Chai Wah Wu, <a href="/A272626/b272626.txt">Table of n, a(n) for n = 1..3003</a>
%H A272626 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 A272626 T(n,k) = 2*T(n,k-1)-T(n,k-2) for k > max(5,(n-1)^2).
%Y A272626 Cf. A271910, A272624, A272625.
%K A272626 nonn,tabl
%O A272626 1,5
%A A272626 _Chai Wah Wu_, May 07 2016