If we take an m X n rectangular grid of points, and choose four of them (in binomial(m*n,4) ways), there are four possibilities: (i) the 4 points are collinear, (ii) 3 points are collinear and one point is not on that line, (iii) 3 points form a triangle of positive area and the other point is in the interior of that triangle, (iv) the 4 points form a convex quadrilateral of nonzero area. As a function of m and n, what are these numbers? This must be a classical problem, but I don't have enough data to check in the OEIS. (It might be called the "moduli space" of 4-tuples from an m X n grid.) I would like the 4 tables of numbers, and exact and/or asymptotic formulas. Which is more likely, (iii) or (iv)? I just looked at what happens if we choose three rather than four points. Now there are only two cases, collinear or not. This produces two triangles of numbers, which are now A334704 and A334705. E.g. A334704(m,n) is the number of ways to choose 3 collinear points from an m X n grid, for m >= n >= 1. Both triangles need more terms, and are lacking exact formulas (or generating functions). Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com