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- W3209053967 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)." @default.
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- W3209053967 date "2021-12-01" @default.
- W3209053967 modified "2023-09-27" @default.
- W3209053967 title "On the co-complex-type <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:mi>k</mml:mi></mml:math>-Fibonacci numbers" @default.
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- W3209053967 doi "https://doi.org/10.1016/j.chaos.2021.111522" @default.
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