Some Properties of Sums Involving Pell Numbers

Some Basic Properties and a Two-by-Two Matrix Involving the k- Pell Numbers

In this paper we consider the k-Pell numbers sequence and present some properties involving the k-Pell numbers. The theoretical basis of using generating matrices for deriving the explicit formula for the term of order n of the k-Pell numbers sequence and also to get the well-known Cassini’s identity using linear algebra. Mathematics Subject Classification: 11B37, 05A15, 11B83.

Some Properties of Generalized Third Order Pell Numbers

This paper considers some properties of the third order recursive sequence defined by the linear recurrence relation , 2 , 1 , 0 , 3 , 2 3 , 2 , , = ≥ + = − − m n w w w n m n m m n m , with appropriate initial conditions. The present work follows on from the case m = 0 (Shannon et al). Relationships with the well-known sequences of Fibonacci, Lucas and Pell are developed. The motivation for the...

Some New Finite Sums Involving Generalized Fibonacci And Lucas Numbers

Tiling Proofs of Recent Sum Identities Involving Pell Numbers

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 the electronic journal of combinatorics 13 (2006), #R00 1 results by in...

Arithmetic properties of q-Fibonacci numbers and q-pell numbers

We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.