On the co-complex-type k-Fibonacci numbers
- Publisher:
- Elsevier BV
- Publication Type:
- Journal Article
- Citation:
- Chaos, Solitons and Fractals, 2021, 153, pp. 111522
- Issue Date:
- 2021-12-01
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| Filename | Description | Size | |||
|---|---|---|---|---|---|
| 1-s2.0-S0960077921008766-main.pdf | Published version | 485.29 kB |
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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).
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