The number of rectangles (orthogonal or not) with corners on an n X n grid of points.

Terms

a(0) =0a(1) =1a(2) =10a(3) =44a(4) =130a(5) =313a(6) =640a(7) =1192a(8) =2044a(9) =3305a(10) =5078a(11) =7524a(12) =10750a(13) =14993a(14) =20388a(15) =27128a(16) =35448a(17) =45665a(18) =57922a(19) =72636a(20) =89970a(21) =110297a(22) =133976a(23) =161440a(24) =192860a(25) =228857a(26) =269758a(27) =316012a(28) =367974a(29) =426417