Article
2022
·
0 citations
THE HYPERBOLIC-TYPE <i>k</i>-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 D-2m, (m >= 2) with respect to the generating pairs (x, y) and (y, x).
Keywords
hyperbolic number
hyperbolic-type sequence
group
matrix
period
LUCAS
NUMBERS
WoS Categories
Thermodynamics
Citation
- Journal
- THERMAL SCIENCE
- Year
- 2022
- Volume
- 26
- Pages
- S551-S558
- ISSN
- 0354-9836
- eISSN
- 2334-7163
- DOI
- 10.2298/TSCI22S2551T
- WoS UID
- WOS:000921231700006