A334710 Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of ways to select four points from an n X k grid so that three of them form a triangle of nonzero area and the extra point is on one of the edges of the triangle.
0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 32, 48, 32, 0, 0, 100, 168, 168, 100, 0, 0, 240, 456, 532, 456, 240, 0, 0, 490, 990, 1312, 1312, 990, 490, 0, 0, 896, 1920, 2652, 3088, 2652, 1920, 896, 0, 0, 1512, 3360, 4972, 5964, 5964, 4972, 3360, 1512, 0, 0, 2400, 5520, 8420, 10816, 11340, 10816, 8420, 5520, 2400, 0
Offset: 1
Examples
The initial rows of the array are: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... 0, 0, 6, 32, 100, 240, 490, 896, 1512, 2400, 3630, 5280, ... 0, 6, 48, 168, 456, 990, 1920, 3360, 5520, 8550, 12720, 18216, ... 0, 32, 168, 532, 1312, 2652, 4972, 8420, 13452, 20480, 29980, 42288, ... 0, 100, 456, 1312, 3088, 5964, 10816, 17768, 27840, 41652, 60040, 83448, ... 0, 240, 990, 2652, 5964, 11340, 20142, 32436, 50004, 73704, 105282, 144936, ... 0, 490, 1920, 4972, 10816, 20142, 35264, 55916, 84960, 123690, 174976, 238512, ... 0, 896, 3360, 8420, 17768, 32436, 55916, 88088, 132708, 191588, 268972, 363876, ... 0, 1512, 5520, 13452, 27840, 50004, 84960, 132708, 198912, 285312, 397968, 534888, ... 0, 2400, 8550, 20480, 41652, 73704, 123690, 191588, 285312, 407744, 566046, 757008, ... ... The initial antidiagonals are: 0 0, 0 0, 0, 0 0, 6, 6, 0 0, 32, 48, 32, 0 0, 100, 168, 168, 100, 0 0, 240, 456, 532, 456, 240, 0 0, 490, 990, 1312, 1312, 990, 490, 0 0, 896, 1920, 2652, 3088, 2652, 1920, 896, 0 0, 1512, 3360, 4972, 5964, 5964, 4972, 3360, 1512, 0 0, 2400, 5520, 8420, 10816, 11340, 10816, 8420, 5520, 2400, 0 0, 3630, 8550, 13452, 17768, 20142, 20142, 17768, 13452, 8550, 3630, 0 ...
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