<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways. In addition, formulas and identities involving these number sequences have been presented. In this paper, we aim at establishing new classes of octonion numbers associated with the third order Jacobsthal and third order Jacobsthal-Lucas numbers. We introduce the third order Jacobsthal octonions and the third order Jacobsthal-Lucas octonions and give some of their properties. We derive the relations between third order Jacobsthal octonions and third order Jacobsthal-Lucas octonions.</p></abstract>

Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways. In addition, formulas and identities involving these number sequences have been presented. In this paper, we aim at establishing new classes of octonion numbers associated with the third order Jacobsthal and third order Jacobsthal-Lucas numbers. We introduce the third order Jacobsthal octonions and the third order Jacobsthal-Lucas octonions and give some of their properties. We derive the relations between third order Jacobsthal octonions and third order Jacobsthal-Lucas octonions.

The Third Order Jacobsthal Octonions: Some Combinatorial Properties

Pontificia Universidad Católica de Valparaíso

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"The Third Order Jacobsthal Octonions: Some Combinatorial Properties"}

Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors...

The Third Order Jacobsthal Octonions: Some Combinatorial Properties

Published Online: Dec 31, 2018

Page range: 57 - 72

Received: Oct 16, 2017

Accepted: Oct 31, 2017

DOI: https://doi.org/10.2478/auom-2018-0033

Keywords
Third order Jacobsthal numbers, third order Jacobsthal-Lucas numbers, third order Jacobsthal octonions, third order Jacobsthal-Lucas octonions, octonion algebra

© 2018 Gamaliel Cerda-Morales, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Third Order Jacobsthal Octonions: Some Combinatorial Properties

Published Online: Dec 31, 2018

Page range: 57 - 72

Received: Oct 16, 2017

Accepted: Oct 31, 2017

DOI: https://doi.org/10.2478/auom-2018-0033

KeywordsThird order Jacobsthal numbers, third order Jacobsthal-Lucas numbers, third order Jacobsthal octonions, third order Jacobsthal-Lucas octonions, octonion algebra

© 2018 Gamaliel Cerda-Morales, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Third order Jacobsthal numbers, third order Jacobsthal-Lucas numbers, third order Jacobsthal octonions, third order Jacobsthal-Lucas octonions, octonion algebra