On a generalization of the Gadovan numbers

Abstract

In this paper, we define (k, l)-Gadovan numbers. We give the Binet-like formula, the generating functions, the exponential generating function of the (k, l)-Gadovan numbers. Also, we derive Cassinilike identity, Catalan-like identity, Vajda-like identity, Honsberger-like identity and D'ocagne-like identity for the (k, l)-Gadovan numbers.

Keywords

• gadovan numbers
• k-gadovan numbers
• binet formula
• generating functions
• cassini identity
• catalan identity