On the generalized Fibonacci and Lucas 2^k−ions

Sure Köme and Hafize Kirik
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367-8275
Volume 26, 2020, Number 4, Pages 173–186
DOI: 10.7546/nntdm.2020.26.4.173-186
Full paper (PDF, 156 Kb)

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Authors and affiliations

Sure Köme
Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Turkey

Hafize Kirik
Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Turkey

Abstract

This study introduces the modified generalized Fibonacci and Lucas 2^k−ions which are the generalizations of several quaternions, octonions and higher order dimensional algebras. We give the generating functions, the Binet formulas and well-known identities such as Catalan’s identity and Cassini’s identity for the modified generalized Fibonacci and Lucas 2^k−ions.

Keywords

• Modified generalized Fibonacci sequence
• Modified generalized Lucas sequence
• Recurrence relations
• 2^k−ions

2010 Mathematics Subject Classification

• 11B39
• 05A15

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