On a New One Parameter Generalization of Pell Numbers

Abstract

In this paper we present a new one parameter generalization of the classical Pell numbers. We investigate the generalized Binet’s formula, the generating function and some identities for r-Pell numbers. Moreover, we give a graph interpretation of these numbers.

Keywords

• Pell numbers
• generalized Pell numbers
• Binet’s formula
• generating function
• Merrifield_Simmons index
• 11B37
• 05C69
• 05A15
• 11B39