On Generalized Pell Numbers Generated by Fibonacci and Lucas Numbers

Abstract

In this paper we introduce a new kind of distance Pell numbers which are generated using the classical Fibonacci and Lucas numbers. Generalized companion Pell numbers is closely related to distance Pell numbers which were introduced in $[12]$. We present some relations between distance Pell numbers, distance companion Pell numbers and their connections with the Fibonacci numbers. To study properties of these numbers we describe their graph interpretations which in the special case gives a distance generalization of the Jacobsthal numbers. We also use the concept of a lexicographic product of graphs to obtain a new interpretation of distance Jacobsthal numbers.