Fügen Torunbalcı Aydın

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 1, Pages 120—135

DOI: 10.7546/nntdm.2018.24.1.120-135

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## Details

### Authors and affiliations

Fügen Torunbalcı Aydın

*Yildiz Technical University
Faculty of Chemical and Metallurgical Engineering
Department of Mathematical Engineering
Davutpasa Campus, 34220, Esenler, Istanbul, Turkey
*

### Abstract

In this paper, the generalized Jacobsthal and generalized complex Jacobsthal and generalized dual Jacobsthal sequences using the Jacobsthal numbers are investigated. Also, special cases of these sequences are investigated. Furthermore, recurrence relations, vectors, the golden ratio and Binet’s formula for the generalized Jacobsthal sequences and generalized dual Jacobsthal sequences are given.

### Keywords

- Jacobsthal number
- Jacobsthal–Lucas number
- Jacobsthal sequence
- Generalized Jacobsthal sequence
- Generalized complex Jacobsthal sequence
- Generalized dual Jacobsthal sequence

### 2010 Mathematics Subject Classification

- 11B37
- 11B50
- 11R52

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## Cite this paper

Aydın, F. T. (2018). On generalizations of the Jacobsthal sequence. Notes on Number Theory and Discrete Mathematics, 24(1), 120-135, doi: 10.7546/nntdm.2018.24.1.120-135.