Mark Kim

Exact Counting of Right Triangles with Vertices at the Nodes of an n x n Grid: Algorithms of Complexity O(n^(3/2+eps)) and O(n log^2 n).

This paper considers the exact computation of the number R(n) of right triangles with vertices at the nodes of an n x n grid (sequence A077435 in the OEIS). A formula is obtained in the form of a fourfold sum, R(n) = 4S^2 + 4W, over p,q,g,mu >= 1 with gcd(p,q)=1. The summand is s...

Recurrent Computation of Alternating Moments of Squared Binomial Coefficients

This paper addresses the computation of the alternating sum of squared binomial coefficients weighted by powers of integer indices. We describe an efficient exact method based on the derivatives of a finite hypergeometric polynomial and Stirling numbers of the second kind. A two-...