Karen S. Briggs^{1}, David P. Little^{2}, and James A. Sellers^{2}

^{1}Department of Mathematics and Computer Science, North Georgia
College and State
University, 82
College Circle, Dahlonega, GA 30597, USA

kbriggs@northgeorgia.edu

^{2}Department 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)