On dual Horadam octonions

Nayil Kılıç
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 1, Pages 137–149
DOI: 10.7546/nntdm.2019.25.1.137-149
Full paper (PDF, 294 Kb)

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Authors and affiliations

Nayil Kılıç
Department of Mathematical Education
Hasan Ali Yücel Education Faculty, Istanbul University-Cerrahpaşa
34470, Fatih, Istanbul, Turkey

Abstract

In this paper, we introduce the dual Horadam octonions, we give the Binet formula, generating function, exponential generating function, summation formula, Catalan’s identity, Cassini’s identity and d’Ocagne’s identity of dual Horadam octonions. Employing these results, we present the Binet formula, generating function, summation formula, Catalan, Cassini and d’Ocagne identities for dual Fibonacci, dual Lucas, dual Jacobsthal, dual Jacobsthal–Lucas, dual Pell and dual Pell–Lucas octonions. So we generalize results that were obtained earlier by scientists. Finally, we introduce the matrix generator for dual Horadam octonions and this generator gives the Cassini formula for the dual Horadam octonions.

Keywords

• Generating functions
• Fibonacci and Lucas numbers and generalizations
• Octonions
• Horadam sequence

2010 Mathematics Subject Classification

• 05A15
• 11B39
• 17A20
• 11B83

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