On (<i>k</i>,<i>p</i>)-Fibonacci Numbers

Abstract

In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously. We prove some identities which generalize well-known relations for Fibonacci numbers, Pell numbers and their generalizations. A matrix representation for generalized Fibonacci numbers is given, too.

Keywords

• Fibonacci numbers
• Pell numbers
• Narayana numbers