2017/10/02 by Gamaliel Cerda-Morales · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Algebra over a field #Fibonacci number #Fibonacci polynomials #Order (exchange) #Recurrence relation #Third order #math.RA #msc:05A15 #msc:11B39 #msc:11R52
paper · pdf · doi:10.2478/auom-2018-0033
published as An. St. Univ. Ovidius Constanta 26(3), (2018), 57--71
arxiv created 2017/10/02 · openalex created_date 2017/10/20 · openalex publication_date 2018/12/01 · arxiv updated 2018/12/21 · openalex updated_date 2026/08/05
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.