Jacobsthal Numbers and Alternating Sign Matrices

Authors

Darrin D. Frey, Cedarville UniversityFollow
James A. Sellers

Document Type

Article

Publication Date

2000

Journal Title

Journal of Integer Sequences

Volume

3

Issue

2

First Page

1

Last Page

15

Abstract

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.

Keywords

Alternating sign matrices, Jacobsthal numbers

Recommended Citation

Frey, D. D. & Sellers, J. A. (2000). Jacobsthal Numbers and Alternating Sign Matrices. Journal of Integer Sequence, 3.