The Hosoya-type Pell r-lengths of certain 2-generator groups

Ömür Deveci and Dürdane Banu Arıkanoğlu
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 3, Pages 514–525
DOI: 10.7546/nntdm.2026.32.3.514-525
Full paper (PDF, 238 Kb)

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Authors and affiliations

Ömür Deveci
Department of Mathematics, Faculty of Science and Letters, Kafkas University
Kafkas 36100, Turkey

Dürdane Banu Arıkanoğlu
Department of Mathematics, Faculty of Science and Letters, Kafkas University
Kafkas 36100, Turkey

Abstract

In this paper, we give the lengths of the periods of the Hosoya-type Pell -orbits of the dihedral group , the semidihedral group and the generalized quaternion group by using some special recurrence sequences.

Keywords

• Hosoya-type Pell r-orbit
• Matrix
• Group
• Period

2020 Mathematics Subject Classification

• 11B39
• 11B50
• 11C20
• 11K31
• 20F05
• 43A30

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Manuscript history

• Received: 16 April 2026
• Revised: 14 October 2026
• Accepted: 16 October 2026
• Online First: 20 October 2026

Copyright information

Ⓒ 2026 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).