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Article
Jacobsthal Numbers and Alternating Sign Matrices
Journal of Integer Sequences
  • Darrin D. Frey, Cedarville University
  • James A. Sellers
Document Type
Article
Publication Date
1-1-2000
Disciplines
Keywords
  • Alternating sign matrices,
  • Jacobsthal numbers
Abstract

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.

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