The hybrid numbers of Padovan and some identities

Milena Carolina dos Santos Mangueira; Renata Passos Machado Vieira; Francisco Régis Vieira Alves; Paula Maria Machado Cruz Catarino

Published: 2020-07-16

Vol. 34 No. 2 (2020)

The hybrid numbers of Padovan and some identities

Milena Carolina dos Santos Mangueira

, Renata Passos Machado Vieira , Francisco Régis Vieira Alves , Paula Maria Machado Cruz Catarino

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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dos Santos Mangueira, M. C., Passos Machado Vieira, R., Régis Vieira Alves, F., & Machado Cruz Catarino, P. M. (2020). The hybrid numbers of Padovan and some identities. Annales Mathematicae Silesianae, 34(2), 256–267. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13615

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Milena Carolina dos Santos Mangueira

milenacarolina24@gmail.com
https://orcid.org/0000-0002-4446-155X

Affiliation:

Federal Institute of Ceará, Scholarship of Coordination for the Coordination of Superior Level Staff Improvement (CAPES), Brazil Brazil

Renata Passos Machado Vieira

Affiliation:

Federal Institute of Ceará, Brazil Brazil

Francisco Régis Vieira Alves

Affiliation:

Federal Institute of Ceará, Scholarship of National Council for Scientific and Technological Development (CNPq), Brazil Brazil

Paula Maria Machado Cruz Catarino

Affiliation:

University of Trás-os-Montes and Alto Douro, Portugal Portugal

Vol. 34 No. 2 (2020)
Published: 2020-09-01

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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