<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

Published Online: Apr 22, 2017

Page range: 201 - 212

Received: Jan 01, 2014

Accepted: Jun 01, 2014

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

Keywords
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

Published Online: Apr 22, 2017

Page range: 201 - 212

Received: Jan 01, 2014

Accepted: Jun 01, 2014

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

Keywordsk-Fibonacci numbers, k-Lucas numbers, quaternions, generating function

© 2017

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

Keywords
k-Fibonacci numbers, k-Lucas numbers, quaternions, generating function