Tiling Proofs of Recent Sum Identities Involving Pell Numbers

Authors

Arthur T. Benjamin, Harvey Mudd CollegeFollow
Sean S. Plott '08, Harvey Mudd CollegeFollow
James A. Sellers, Pennsylvania State University - Main Campus

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

10-2008

Abstract

In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their proofs relied heavily on the Binet formula for the Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of a number of the identities.

Comments

First published in Annals of Combinatorics Volume 12, Number 3 (2008), 271-278.

This article is also available at http://www.springerlink.com/content/pn4287381k426n66/.

Rights Information

© 2008 Springer, Part of Springer Science + Business Media

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DOI

10.1007/s00026-008-0350-5

Recommended Citation

Benjamin, A.T., Plott, S.S., & Sellers, J.A. (2008). Tiling proofs of recent sum identities involving Pell numbers. Annals of Combinatorics, 12(3): 271-278. DOI: 10.1007/s00026-008-0350-5.