A320539 (1/2) * number of ways to select 3 distinct collinear points from a rectangle of grid points with side lengths j and k, written as triangle T(j,k), j<=k.
0, 1, 4, 4, 10, 22, 10, 21, 42, 76, 20, 39, 70, 120, 186, 35, 65, 112, 184, 279, 412, 56, 100, 166, 264, 390, 566, 772, 84, 146, 236, 367, 532, 759, 1026, 1356, 120, 205, 324, 494, 704, 991, 1326, 1740, 2224, 165, 278, 432, 647, 913, 1271, 1686, 2196, 2793, 3496
Offset: 1
Examples
The triangle begins:
0
1 4
4 10 22
10 21 42 76
20 39 70 120 186
35 65 112 184 279 412
56 100 166 264 390 566 772
.
a(2) = T(1,2) = 1, because the grid points on the two longer sides of the rectangle are collinear: (0,0) (0,1) (0,2) and (1,0) (1,1) (2,2).
a(3) = T(2,2) = 4, because there are 8 triples of collinear points:
(0,0) (0,1) (0,2),
(0,0) (1,0) (2,0),
(0,0) (1,1) (2,2),
(0,1) (1,1) (2,1),
(0,2) (1,1) (2,0),
(0,2) (1,2) (2,2),
(1,0) (1,1) (1,2),
(2,0) (2,1) (2,2).
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