On the Generalized Fibonacci-circulant-Hurwitz numbers

Ömür Deveci, Zafer Adıgüzel and Taha Doğan
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 1, Pages 179-190
DOI: 10.7546/nntdm.2020.26.1.179-190
Full paper (PDF, 182 Kb)

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Authors and affiliations

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

Zafer Adıgüzel
Department of Mathematics, Faculty of Science and Letters
Kafkas University, 36100, Turkey

Taha Doğan
Department of Mathematics, Faculty of Science and Letters
Kafkas University, 36100, Turkey

Abstract

The theory of Fibonacci-circulant numbers was introduced by Deveci et al. (see [5]).
In this paper, we define the Fibonacci-circulant-Hurwitz sequence of the second kind by Hurwitz matrix of the generating function of the Fibonacci-circulant sequence of the second kind and give a fair generalization of the sequence defined, which we call the generalized Fibonacci-circulant-Hurwitz sequence. First, we derive relationships between the generalized Fibonacci-circulant-Hurwitz numbers and the generating matrices for these numbers. Also, we give miscellaneous properties of the generalized Fibonacci-circulant-Hurwitz numbers such as the Binet formula, the combinatorial, permanental, determinantal representations, the generating function, the exponential representation and the sums.

Keywords

• Fibonacci-circulant-Hurwitz Sequence
• Circulant matrix
• Hurwitz matrix
• Representation

2010 Mathematics Subject Classification

• 11K31
• 11B50
• 11C20
• 20D60

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