This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334708 #32 Jul 09 2025 04:52:45 %S A334708 0,0,0,0,0,0,1,0,0,1,5,2,0,2,5,15,10,3,3,10,15,35,30,15,10,15,30,35, %T A334708 70,70,45,29,29,45,70,70,126,140,105,72,64,72,105,140,126,210,252,210, %U A334708 157,129,129,157,210,252,210,330,420,378,302,248,234,248,302,378,420,330 %N A334708 Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of ways to select four collinear points from an n X k grid. %C A334708 Computed by _Tom Duff_, Jun 15 2020 %H A334708 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 A334708 The initial rows of the array are: %e A334708 0, 0, 0, 1, 5, 15, 35, 70, 126, 210, 330, 495, ... %e A334708 0, 0, 0, 2, 10, 30, 70, 140, 252, 420, 660, 990, ... %e A334708 0, 0, 0, 3, 15, 45, 105, 210, 378, 630, 990, 1485, ... %e A334708 1, 2, 3, 10, 29, 72, 157, 302, 531, 874, 1361, 2028, ... %e A334708 5, 10, 15, 29, 64, 129, 248, 442, 747, 1196, 1825, 2679, ... %e A334708 15, 30, 45, 72, 129, 234, 405, 666, 1065, 1638, 2439, 3510, ... %e A334708 35, 70, 105, 157, 248, 405, 660, 1020, 1545, 2276, 3283, 4605, ... %e A334708 70, 140, 210, 302, 442, 666, 1020, 1524, 2220, 3154, 4412, 6030, ... %e A334708 126, 252, 378, 531, 747, 1065, 1545, 2220, 3156, 4362, 5940, 7923, ... %e A334708 210, 420, 630, 874, 1196, 1638, 2276, 3154, 4362, 5928, 7914, 10350, ... %e A334708 ... %e A334708 The initial antidiagonals are: %e A334708 0 %e A334708 0, 0 %e A334708 0, 0, 0 %e A334708 1, 0, 0, 1 %e A334708 5, 2, 0, 2, 5 %e A334708 15, 10, 3, 3, 10, 15 %e A334708 35, 30, 15, 10, 15, 30, 35 %e A334708 70, 70, 45, 29, 29, 45, 70, 70 %e A334708 126, 140, 105, 72, 64, 72, 105, 140, 126 %e A334708 210, 252, 210, 157, 129, 129, 157, 210, 252, 210 %e A334708 330, 420, 378, 302, 248, 234, 248, 302, 378, 420, 330 %e A334708 ... %Y A334708 The main diagonal is A178256. %Y A334708 Triangles A334708, A334709, A334710, A334711 give the counts for the four possible arrangements of four points. %Y A334708 For three points there are just two possible arrangements: see A334704 and A334705. %K A334708 nonn,tabl %O A334708 1,11 %A A334708 _N. J. A. Sloane_, Jun 15 2020