Journal of Integer Sequences, Vol. 3 (2000), Article 00.2.3

Jacobsthal Numbers and Alternating Sign Matrices

Darrin D. Frey and James A. Sellers
Department of Science and Mathematics
Cedarville College
Cedarville, OH 45314
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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
l = 0
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.

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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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