Jacobsthal numbers and alternating sign matrices
Journal of integer sequences, Tome 3 (2000) no. 2
Let $A(n)$ denote the number of n$\times n$ alternating sign matrices and $J_{m}$ the $m^{th}$ Jacobsthal 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.
@article{JIS_2000__3_2_a2,
author = {Frey, Darrin D. and Sellers, James A.},
title = {Jacobsthal numbers and alternating sign matrices},
journal = {Journal of integer sequences},
year = {2000},
volume = {3},
number = {2},
zbl = {0961.15008},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JIS_2000__3_2_a2/}
}
Frey, Darrin D.; Sellers, James A. Jacobsthal numbers and alternating sign matrices. Journal of integer sequences, Tome 3 (2000) no. 2. http://geodesic.mathdoc.fr/item/JIS_2000__3_2_a2/