The purpose of this paper is twofold; (1) to develop several identities for the Generalized $k$-Pell sequence (including those of Binet, Catalan, Cassini, and d'Ocagne), and (2) to study applications of tridiagonal generating matrices for the $k$-Pell and Generalized $k$-Pell sequences.

In this paper we define some tridiagonal matrices depending of a parameter from which we will find the k-Pell, k-Pell-Lucas and Modified k-Pell numbers. Mathematics Subject Classification: 11B37,… Expand

We obtain the Binet’s formula for k-Pell numbers and as a consequence we get some properties for k-Pell numbers. Also we give the generating function for k-Pell sequences and another expression for… Expand

We obtain the Binet’s formula for k-Pell-Lucas numbers and as a consequence we obtain some properties for k-Pell-Lucas numbers. Also we give the generating function for the k-Pell-Lucas sequences and… Expand

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… Expand

On the generating matrices of the k-Fibonacci numbers, Proyecciones

2013

On the generating matrices of the k-Fibonacci numbers

Proyecciones

2013

The eigenvalues of tridiagonal matrices, course notes for TMA 4205 at Norwegian University of Science and Technology, Department of Mathematical Sciences

2009

Saint Mary's College of California, 1928 Saint Mary's Rd