On properties of generalized Tridovan numbers

Yüksel Soykan, Nejla Özmen and Inci Okumuş
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 571–588
DOI: 10.7546/nntdm.2023.29.3.571-588
Full paper (PDF, 240 Kb)


Authors and affiliations

Yüksel Soykan
Department of Mathematics, Art and Science Faculty, Zonguldak Bülent Ecevit University
67100 Zonguldak, Turkey

Nejla Özmen
Department of Mathematics, Faculty of Art and Science, Duzce University
81620 Konuralp, Duzce, Turkey

Inci Okumuş
Department of Engineering Sciences, Faculty of Engineering, Istanbul University-Cerrahpasa
34320 Istanbul, Turkey


In this paper, we examine generalized Tridovan sequences and treat in detail two cases called Tridovan sequences and Tridovan–Lucas sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences. In addition, we give some identities and matrices related to these sequences.


  • Tridovan numbers
  • Tridovan–Lucas numbers
  • Tetranacci numbers

2020 Mathematics Subject Classification

  • 11B37
  • 11B39
  • 11B83


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Manuscript history

  • Received: 25 September 2022
  • Revised: 28 July 2023
  • Accepted: 14 August 2023
  • Online First: 17 August 2023

Copyright information

Ⓒ 2023 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).

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Cite this paper

Soykan, Y., Özmen, N., Okumuş, I. (2023). On properties of generalized Tridovan numbers. Notes on Number Theory and Discrete Mathematics, 29(3), 571-588, DOI: 10.7546/nntdm.2023.29.3.571-588.

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