A Two-Parameter Generalization of Pell Numbers in Graphs

Urszula Bednarz1, Malgorzata Wolowiec-Musial1
1Rzeszéw University of Technology Faculty of Mathematics and Applied Physics al. Powstaricé6w Warszawy 12, 35-359 Rzeszdw, Poland

Abstract

In this paper we introduce a new kind of two-parameters generalization of Pell numbers. We give two distinct graph interpretations and prove some identities for these numbers. Moreover we define matrix generators and derive the generalized Cassini formula for the introduced numbers.