The hybrid numbers of Padovan and some identities
Abstract
In this article, we will define Padovan’s hybrid numbers, based on the new noncommutative numbering system studied by Özdemir ([7]). Such a system that is a set involving complex, hyperbolic and dual numbers. In addition, Padovan’s hybrid numbers are created by combining this set, satisfying the relation ih = -hi = ɛ+i. Given this, some properties and identities are
shown for these numbers, such as Binet’s formula, generating matrix, characteristic equation, norm, and generating function. In addition, these numbers are extended to the integer field and some identities are made.
Keywords
Binet’s formula; hybrid numbers; Padovan sequence; hybrid Padovan number
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Federal Institute of Ceará, Scholarship of Coordination for the Coordination of Superior Level Staff Improvement (CAPES), Brazil Brazil
https://orcid.org/0000-0002-4446-155X
Federal Institute of Ceará, Brazil Brazil
Federal Institute of Ceará, Scholarship of National Council for Scientific and Technological Development (CNPq), Brazil Brazil
University of Trás-os-Montes and Alto Douro, Portugal Portugal
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