Fundamental properties of extended Horadam numbers

Gülsüm Yeliz Şentürk, Nurten Gürses and Salim Yüce
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 4, Pages 219—235
DOI: 10.7546/nntdm.2021.27.4.219-235
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Authors and affiliations

Gülsüm Yeliz Şentürk
Faculty of Engineering and Architecture, Istanbul Gelisim University,
Department of Computer Engineering, 34310, Istanbul, Turkey

Nurten Gürses
Faculty of Arts and Sciences, Yildiz Technical University,
Department of Mathematics, 34220, Istanbul, Turkey

Salim Yüce
Faculty of Arts and Sciences, Yildiz Technical University,
Department of Mathematics, 34220, Istanbul, Turkey


In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.


  • Horadam number
  • Dual-generalized complex number
  • Hyperbolic-generalized complex number
  • Binet’s formula
  • D’Ocagne’s identity
  • Catalan’s identity
  • Cassini’s identity

2020 Mathematics Subject Classification

  • 11B37
  • 11B39
  • 11K31


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Cite this paper

Şentürk, G. Y., Gürses, N., & Yüce, S. (2021). Fundamental properties of extended Horadam numbers. Notes on Number Theory and Discrete Mathematics, 27(4), 219-235, doi: 10.7546/nntdm.2021.27.4.219-235.

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