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Combinatorial Proofs of Various q-Pell Identities via Tilings
Karen S. Briggs1, David P. Little2, and James A. Sellers2
1Department of Mathematics and Computer Science, North Georgia College and State University, 82 College Circle, Dahlonega, GA 30597, USA
kbriggs@northgeorgia.edu
2Department of Mathematics, Pennsylvania State University, University Park, State College, PA 16802, USA
{dlittle, sellersj}@math.psu.edu
Annals of Combinatorics 14 (4) pp.407-418 December, 2010
AMS Subject Classification: 05A19
Abstract:
Recently, Benjamin, Plott, and Sellers proved a variety of identities involving sums of Pell numbers combinatorially by interpreting both sides of a given identity as enumerators of certain sets of tilings using white squares, black squares, and gray dominoes. In this article, we state and prove q-analogues of several Pell identities via weighted tilings.
Keywords: Pell numbers, combinatorial identities, tilings, q-enumeration

References:

1. Andrews, G.E.: The Theory of Partitions. Addison-Wesley, Reading (1976)

2. Benjamin, A.T., Plott, S.P., Sellers, J.A.: Tiling proofs of recent sum identities involving Pell numbers. Ann. Combin. 12(3), 271--278 (2008)

3. Santos, J.P.O., Sills, A.V.: q-Pell sequences and two identities of V. A. Lebesgue. Discrete Math. 257 125--142 (2002)