De Moivre-type identities for the Jacobsthal numbers

Mücahit Akbiyik and Seda Yamaç Akbiyik
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 3, Pages 95–103
DOI: 10.7546/nntdm.2021.27.3.95-103
Full paper (PDF, 157 Kb)

Details

Authors and affiliations

Mücahit Akbiyik
Department of Mathematics, Beykent University
Büyükçekmece / Istanbul, Turkey

Seda Yamaç Akbiyik
Department of Computer Engineering, Istanbul Gelisim University
Avcılar / Istanbul, Turkey

Abstract

The main aim of this study is to obtain De Moivre-type identities for Jacobsthal numbers. Also, this paper presents a method for constructing the second order Jacobsthal and Jacobsthal third-order numbers and the third-order Jacobsthal and Jacobsthal–Lucas numbers. Moreover, we give some interesting identities, such as Binet’s formulas for some specific third-order Jacobsthal numbers that we derive from De Moivre-type identities.

Keywords

• De Moivre-type identity
• Jacobsthal numbers
• Binet’s formula

2020 Mathematics Subject Classification

• 11B39
• 11B83

References

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