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 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. 7
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Computed by Tom Duff, Jun 15 2020 LINKS EXAMPLE 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 ... CROSSREFS The main diagonal is A334713. Triangles A334708, A334709, A334710, A334711 give the counts for the four possible arrangements of four points. For three points there are just two possible arrangements: see A334704 and A334705. Sequence in context: A055667 A281080 A283347 * A283203 A155742 A005597 Adjacent sequences:  A334707 A334708 A334709 * A334711 A334712 A334713 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jun 15 2020. STATUS approved

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Last modified January 26 07:26 EST 2022. Contains 350573 sequences. (Running on oeis4.)