On Some identities for Generalized Fibonacci and Lucas Sequences with Rational Subscript

Authors

  • Saadet Arslan Department of Secondary Science and Mathematics Education, Necmettin Erbakan University, Konya
  • Fikri Köken Eregli Kemal Akman Vocational School, Necmettin Erbakan University, Konya
  • Youness El Khatabi Department of Mathematics and Informatics, Moulay Ismail University, Beni M'hamed, Meknes

DOI:

https://doi.org/10.26713/jims.v11i1.648

Keywords:

Horadam Sequences, Generalized Fibonacci Sequences, Generalized Lucas Sequences, Matrix Functions

Abstract

In this paper, we exploit general techniques from matrix theory to establish some identities for generalized Fibonacci and Lucas sequences with rationalsubscripts of the forms \(\frac{n}{2}\) and \(\frac{r}{s}\). For this purpose, we consider matrix functions \(X\mapsto X^{n/2}\) (resp. \(X\mapsto X^{r/s}\)) of two special matrices, and discuss whether the \(\frac{n}{2}\) (resp. \(\frac{r}{s}\)) are integers or irreducible fractions.

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References

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Published

2019-03-31
CITATION

How to Cite

Arslan, S., Köken, F., & El Khatabi, Y. (2019). On Some identities for Generalized Fibonacci and Lucas Sequences with Rational Subscript. Journal of Informatics and Mathematical Sciences, 11(1), 41–49. https://doi.org/10.26713/jims.v11i1.648

Issue

Vol. 11 No. 1 (2019)

Section

Research Articles

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