cp's OEIS Frontend

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.

%I A334710 #23 Jul 09 2025 04:52:51
%S A334710 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,
%T A334710 456,240,0,0,490,990,1312,1312,990,490,0,0,896,1920,2652,3088,2652,
%U A334710 1920,896,0,0,1512,3360,4972,5964,5964,4972,3360,1512,0,0,2400,5520,8420,10816,11340,10816,8420,5520,2400,0
%N 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.
%C A334710 Computed by _Tom Duff_, Jun 15 2020
%H A334710 Tom Duff, <a href="/A334708/a334708_3.txt">Data for tables A334708, A334709, A334710, A334711 for grids of size up to 192 X 192</a>
%e A334710 The initial rows of the array are:
%e A334710 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e A334710 0, 0, 6, 32, 100, 240, 490, 896, 1512, 2400, 3630, 5280, ...
%e A334710 0, 6, 48, 168, 456, 990, 1920, 3360, 5520, 8550, 12720, 18216, ...
%e A334710 0, 32, 168, 532, 1312, 2652, 4972, 8420, 13452, 20480, 29980, 42288, ...
%e A334710 0, 100, 456, 1312, 3088, 5964, 10816, 17768, 27840, 41652, 60040, 83448, ...
%e A334710 0, 240, 990, 2652, 5964, 11340, 20142, 32436, 50004, 73704, 105282, 144936, ...
%e A334710 0, 490, 1920, 4972, 10816, 20142, 35264, 55916, 84960, 123690, 174976, 238512, ...
%e A334710 0, 896, 3360, 8420, 17768, 32436, 55916, 88088, 132708, 191588, 268972, 363876, ...
%e A334710 0, 1512, 5520, 13452, 27840, 50004, 84960, 132708, 198912, 285312, 397968, 534888, ...
%e A334710 0, 2400, 8550, 20480, 41652, 73704, 123690, 191588, 285312, 407744, 566046, 757008, ...
%e A334710 ...
%e A334710 The initial antidiagonals are:
%e A334710 0
%e A334710 0, 0
%e A334710 0, 0, 0
%e A334710 0, 6, 6, 0
%e A334710 0, 32, 48, 32, 0
%e A334710 0, 100, 168, 168, 100, 0
%e A334710 0, 240, 456, 532, 456, 240, 0
%e A334710 0, 490, 990, 1312, 1312, 990, 490, 0
%e A334710 0, 896, 1920, 2652, 3088, 2652, 1920, 896, 0
%e A334710 0, 1512, 3360, 4972, 5964, 5964, 4972, 3360, 1512, 0
%e A334710 0, 2400, 5520, 8420, 10816, 11340, 10816, 8420, 5520, 2400, 0
%e A334710 0, 3630, 8550, 13452, 17768, 20142, 20142, 17768, 13452, 8550, 3630, 0
%e A334710 ...
%Y A334710 The main diagonal is A334713.
%Y A334710 Triangles A334708, A334709, A334710, A334711 give the counts for the four possible arrangements of four points.
%Y A334710 For three points there are just two possible arrangements: see A334704 and A334705.
%K A334710 nonn,tabl
%O A334710 1,8
%A A334710 _N. J. A. Sloane_, Jun 15 2020