A new quadra polynomial sequence

Emre Sevgi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 3, Pages 595–601
DOI: 10.7546/nntdm.2024.30.3.595-601
Full paper (PDF, 194 Kb)

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Authors and affiliations

Emre Sevgi
Department of Mathematics, Gazi University
Ankara, Türkiye

Abstract

In this paper, we define a new quadra polynomial sequence by using Özkoç numbers as the coefficients. Then, we derive some properties for this polynomial sequence by the help of Fibonacci and Pell polynomials. Additionally, we attempt to define the companion matrix of this polynomial sequence.

Keywords

  • Fibonacci number
  • Pell number
  • Generating function
  • Binet formula

2020 Mathematics Subject Classification

  • 11B37
  • 11B39
  • 11B83

References

  1. Horadam, A., & Mahon, J. (1985). Pell and Pell–Lucas polynomials. The Fibonacci Quarterly, 23(1), 7–20.
  2. Horzum, T., & Kocer, E. G. (2009). On some properties of Horadam polynomials. International Mathematical Forum, 4(25), 1243–1252.
  3. Kızılateş, C. (2017). On the quadra Jacobsthal–Lucas numbers. Karaelmas Fen ve Mühendislik Dergisi, 7(2), 619–621.
  4. Kızılateş, C., Tuglu, N., & Çekim, B. (2017). Binomial transforms of quadrapell sequences and quadrapell matrix sequences. Journal of Science and Arts, 38(1), 69–80.
  5. Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications. John Wiley and Sons Inc., New York.
  6. Özkoç, A. (2015). Some algebraic identities on quadra Fibona–Pell integer sequence. Advances in Difference Equations, 148, 1–10.
  7. Tasci, D. (2009). On quadrapell numbers and quadrapell polynomials. Hacettepe Journal of Mathematics and Statistics, 38(3), 265–275.
  8. Tekcan, A., Özkoç, A., Engür, M., & Özbek, M. E. (2016). On algebraic identities on a new integer sequence with four parameters. Ars Combinatoria, 127, 225–238.

Manuscript history

  • Received: 12 March 2024
  • Revised: 21 May 2024
  • Accepted: 18 October 2024
  • Online First: 22 October 2024

Copyright information

Ⓒ 2024 by the Author.
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

Sevgi, E. (2024). A new quadra polynomial sequence. Notes on Number Theory and Discrete Mathematics, 30(3), 595-601, DOI: 10.7546/nntdm.2024.30.3.595-601

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