Physical Sciences and Mathematics Commons^™

Jacobsthal Numbers And Alternating Sign Matrices, Darrin D. Frey, James A. Sellers

Science and Mathematics Faculty Publications

Let A(n) denote the number of n×n alternating sign matrices and J_m the m^thJacobsthal number. It is known that

A(n) = n-1 Õ l = 0 (3l+1)!(n+l)! .

The values of A(n) are in general highly composite. The goal of this paper is to prove that A(n) is odd if and only if n is a Jacobsthal number, thus showing that A(n) is odd infinitely often.