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February 2006 Some Properties of Sums Involving Pell Numbers
Sergio Falcón Santana, José Luis Díaz-Barrero
Missouri J. Math. Sci. 18(1): 33-40 (February 2006). DOI: 10.35834/2006/1801033

Abstract

In this note we prove that for all positive integers $n$, the sum $S_{4n+1}$ of the first $4n+1$ Pell numbers is a perfect square. As a consequence, an identity involving binomial coefficients and Pell numbers is given. Also, sums of an even and odd number of terms of odd order are evaluated and some divisibility properties are obtained.

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Sergio Falcón Santana. José Luis Díaz-Barrero. "Some Properties of Sums Involving Pell Numbers." Missouri J. Math. Sci. 18 (1) 33 - 40, February 2006. https://doi.org/10.35834/2006/1801033

Information

Published: February 2006
First available in Project Euclid: 3 August 2019

zbMATH: 1137.05009
MathSciNet: MR2650060
Digital Object Identifier: 10.35834/2006/1801033

Subjects:
Primary: 05A19
Secondary: 11B39

Rights: Copyright © 2006 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.18 • No. 1 • February 2006
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