On some combinatorial properties of bihyperbolic numbers of the Lucas type.

Abstract

In the literature until today, many authors have studied special sequences in different number systems. In this article, we examined the combinatorial properties of Lucas-type bihyperbolic numbers. Lucas bihyperbolic numbers were studied by Azak \cite{aza} in 2020. For this reason, only bihyperbolic Jacobsthal-Lucas and Pell-Lucas numbers were examined using Jacobsthal-Lucas and Pell-Lucas numbers. We also give some algebraic properties of bihyperbolic Jacobsthal-Lucas and bihyperbolic Pell-Lucas numbers, such as the recursion relation, generating function, Binet formula, D'Ocagne identity, Cassini identity, Catalan identity and Honsberger identity.