On Distance Pell Numbers and Their Connections with Fibonacci Numbers

Abstract

In this paper we introduce a new kind of generalized Pell numbers. This generalization is introduced in the distance sense. We give different interpretations and representations of these numbers.We present relations between distance Pell numbers and Fibonacci numbers. Moreover we describe graph interpretations of distance Pell numbers. These graphs interpretations in the natural way imply a new kind of generalized Jacobsthal numbers.