# The Fibonacci–Circulant Sequences and Their Applications

@article{Deveci2017TheFS, title={The Fibonacci–Circulant Sequences and Their Applications}, author={{\"O}m{\"u}r Deveci and Erdal Karaduman and Colin M. Campbell}, journal={Iranian Journal of Science and Technology, Transactions A: Science}, year={2017}, volume={41}, pages={1033-1038} }

In this paper, we define the recurrence sequences using the Circulant matrices which are obtained from the characteristic polynomial of the Fibonacci sequence, and then, we give miscellaneous properties of these sequences. In addition, we consider the cyclic groups which are generated by the generating matrices and the auxiliary equations of the defined recurrence sequences, and then, we study the orders of these cyclic groups. Furthermore, we extend the defined sequences to groups. Finally, we…

## 5 Citations

The complex-type k-Fibonacci sequences and their applications

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Abstract In this article, we define the complex-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the complex-type k-Fibonacci numbers. Also, we obtain…

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Abstract We define the Gauss Fibonacci polynomials. Then we give a formula for the Gauss Fibonacci polynomials by using the Fibonacci polynomials. The Gauss Lucas polynomials are described and the…

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In this paper, we obtain explicit Euclidean norm, eigenvalues, spectral norm and determinant of circulant matrix with the generalized Tribonacci (generalized (r, s, t)) numbers. We also present the…

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In this study, a matrix $$R_{L}$$RL is defined by the properties associated with the Pascal matrix, and two closed-form expressions of the matrix function $$f(R_{L})=R_{L}^{n}$$f(RL)=RLn are…

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