Abstract
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 obtain the lengths of the periods of the extended sequences in the polyhedral groups (2, 3, 3) and (n, 2, 2) as applications of the results obtained.
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Acknowledgements
This Project was supported by the Commission for the Scientific Research Projects of Kafkas University. The Project Number 2014-FEF-34.
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Deveci, Ö., Karaduman, E. & Campbell, C.M. The Fibonacci–Circulant Sequences and Their Applications. Iran J Sci Technol Trans Sci 41, 1033–1038 (2017). https://doi.org/10.1007/s40995-017-0317-7
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DOI: https://doi.org/10.1007/s40995-017-0317-7