Jacobsthal Numbers and Alternating Sign Matrices
Darrin D. Frey and James A. Sellers
Department of Science and Mathematics
Cedarville College
Cedarville, OH 45314
Email addresses:
freyd@cedarville.edu and
sellersj@cedarville.edu
Abstract:
Let A(n) denote the number of n×n alternating sign matrices and
Jm the mth 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.
Full version: pdf,
dvi,
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(Concerned with sequences
A001045,
A001859,
A005130.)
Received Jan. 13, 2000; published in Journal of Integer Sequences June 1, 2000.
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