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 A320539 #8 Oct 22 2018 14:28:24 %S A320539 0,1,4,4,10,22,10,21,42,76,20,39,70,120,186,35,65,112,184,279,412,56, %T A320539 100,166,264,390,566,772,84,146,236,367,532,759,1026,1356,120,205,324, %U A320539 494,704,991,1326,1740,2224,165,278,432,647,913,1271,1686,2196,2793,3496 %N 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. %C A320539 Permutations of the 3 points are not counted separately. %e A320539 The triangle begins: %e A320539 0 %e A320539 1 4 %e A320539 4 10 22 %e A320539 10 21 42 76 %e A320539 20 39 70 120 186 %e A320539 35 65 112 184 279 412 %e A320539 56 100 166 264 390 566 772 %e A320539 . %e A320539 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). %e A320539 a(3) = T(2,2) = 4, because there are 8 triples of collinear points: %e A320539 (0,0) (0,1) (0,2), %e A320539 (0,0) (1,0) (2,0), %e A320539 (0,0) (1,1) (2,2), %e A320539 (0,1) (1,1) (2,1), %e A320539 (0,2) (1,1) (2,0), %e A320539 (0,2) (1,2) (2,2), %e A320539 (1,0) (1,1) (1,2), %e A320539 (2,0) (2,1) (2,2). %Y A320539 A000292, A320540, A320541, A320543. %K A320539 nonn,tabl %O A320539 1,3 %A A320539 _Hugo Pfoertner_, Oct 15 2018