THERMAL SCIENCE

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Sait Tas

THE HYPERBOLIC-TYPE K-FIBONACCI SEQUENCES AND THEIR APPLICATIONS

ABSTRACT
In this study, we define hyperbolic-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the hyperbolic-type k-Fibonacci numbers. In addition, we study the hyperbolic-type k-Fibonacci sequence modulo m and then we give periods of the Hperbolic-type k-Fibonacci sequences for any k and m which are related the periods of the k-step Fibonacci sequences modulo m. Furthermore, we extend the hyperbolic-type k-Fibonacci sequences to groups. Finally, we obtain the periods of the hyperbolic-type 2-Fibonacci sequences in the dihedral group D2m, (m ≥ 2) with respect to the generating pairs (x,y) and (y, x).
KEYWORDS
hyperbolic number, hyperbolic-type sequence, group, matrix, period
PAPER SUBMITTED: 2022-08-15
PAPER REVISED: 2022-09-10
PAPER ACCEPTED: 2022-09-20
PUBLISHED ONLINE: 2023-01-29
DOI REFERENCE: https://doi.org/10.2298/TSCI22S2551T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 2, PAGES [551 - 558]
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The hyperbolic-type k-Fibonacci sequences and their applications

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