- Alternating sign matrices,
- Jacobsthal numbers
Let A(n) denote the number of n×n alternating sign matrices and Jm the mthJacobsthal 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.