On the co-complex-type k-Fibonacci numbers

Ömür Deveci, Sakine Hulku and Anthony G. Shannon

Chaos, Solitons & Fractals, 2021, vol. 153, issue P2

Abstract: In this paper, we define the co-complex-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the co-complex-type k-Fibonacci numbers. Also, we produce various properties of the co-complex-type k-Fibonacci numbers such as the generating matrices, the Binet formulas, the combinatorial, permanental and determinantal representations, and the finite sums by matrix methods. In addition, we study the co-complex-type k-Fibonacci sequence modulo m and then we give some results concerning the periods and the ranks of the co-complex-type k-Fibonacci sequences for any k and m. Furthermore, we extend the co-complex-type k-Fibonacci sequences to groups. Finally, we obtain the periods of the co-complex-type 2-Fibonacci sequences in the semidihedral group SD2m, (m≥4) with respect to the generating pair (x,y).

Keywords: The co-complex-type numbers; Matrix; Representation; Group; Period; Rank (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008766

DOI: 10.1016/j.chaos.2021.111522

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