On the Structure and Generalization of Bihyperbolic Leonardo Sequences

Resumo

In this paper, we give some properties of the bihyperbolic Leonardo numbers, among others the Binet formula, generating function formula and the general bilinear index-reduction formula which implies d'Ocagne, Vajda, Halton, Catalan, and Cassini identities. We also give the matrix representation and some sum formulas of the bihyperbolic Leonardo numbers. Moreover, we present a one-parameter generalization of the bihyperbolic Leonardo numbers and their properties.