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)**

## Details

### 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

*−ions.*

^{k}### Keywords

- Modified generalized Fibonacci sequence
- Modified generalized Lucas sequence
- Recurrence relations
- 2
−ions^{k}

### 2010 Mathematics Subject Classification

- 11B39
- 05A15

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## Cite this paper

Köme, S., & Kirik, H. (2020). On the generalized Fibonacci and Lucas 2* ^{k}*−ions.

*Notes on Number Theory and Discrete Mathematics*, 26 (4), 173-186, DOI: 10.7546/nntdm.2020.26.4.173-186.