<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In addition, we derive some sums formulas and identities such as Cassini’s identity.</p></abstract>

In this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In addition, we derive some sums formulas and identities such as Cassini’s identity.

Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions

Instituto de Matemáticas y sus Aplicaciones, Universidad Sergio Arboleda, Bogotá,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions"}

In this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In...

Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions

Publié en ligne: 22 avr. 2017

Pages: 201 - 212

Reçu: 01 janv. 2014

Accepté: 01 juin 2014

DOI: https://doi.org/10.1515/auom-2015-0037

Mots clés
k-Fibonacci numbers, k-Lucas numbers, quaternions, generating function

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions

Publié en ligne: 22 avr. 2017

Pages: 201 - 212

Reçu: 01 janv. 2014

Accepté: 01 juin 2014

DOI: https://doi.org/10.1515/auom-2015-0037

Mots clésk-Fibonacci numbers, k-Lucas numbers, quaternions, generating function

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
k-Fibonacci numbers, k-Lucas numbers, quaternions, generating function