On Vietoris' hybrid number sequence

Abstract

This work is intended to establish a relation between Vietoris' sequence, which is a rational sequence, and hybrid numbers. Then it provides some characteristic properties of the hybrid numbers with Vietoris' number coefficients. Some relations between this hybrid number and its norm, the recurrence relations, the generating function, Binet-like formula and Catalan -like identities are also indicated. Furthermore, a determinantal approach is presented to obtain elements of Vietoris' hybrid number sequence.