# 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}
}
• Published 1 November 2017
• Mathematics
• Iranian Journal of Science and Technology, Transactions A: Science
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…
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