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## On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix

#### Yasemin Taşyurdu [1] , Zülküf Dilmen [2]

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In this study,  Fibonacci sequence was defined over an arbitrary ring and its some properties are investigated. The terms of this sequence are derivated by Tridiagonal determinant of the matrix. It was shown that this sequence is periodic and their period is obtained. It was shown that the sequence obtained by reducing modulo  coefficient and exponent of each Fibonacci sequence in arbitrary rings is periodic. It was seen that order of cyclic group generated with matrix   is equal to the period of this sequence where  are arbitrary elements of the ring.  Also, the period of this sequence is compared with Wall number of Fibonacci sequence and it was shown that this period always was an even number.

Fibonacci Sequence, Finite Ring, Period
• Taşyurdu, Y.; Gültekin, İ., The Period of Fibonacci Sequences Over The Finite Field of Order p^2, New Trends in Mathematical Sciences. 2016; 4, 248-255.
Subjects Engineering Articles Author: Yasemin Taşyurdu Author: Zülküf Dilmen
 Bibtex @research article { cbayarfbe302663, journal = {Celal Bayar University Journal of Science}, issn = {1305-130X}, eissn = {1305-1385}, address = {Celal Bayar University}, year = {2017}, volume = {13}, pages = {165 - 169}, doi = {10.18466/cbayarfbe.302663}, title = {On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix}, key = {cite}, author = {Taşyurdu, Yasemin and Dilmen, Zülküf} } APA Taşyurdu, Y , Dilmen, Z . (2017). On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. Celal Bayar University Journal of Science, 13 (1), 165-169. DOI: 10.18466/cbayarfbe.302663 MLA Taşyurdu, Y , Dilmen, Z . "On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix". Celal Bayar University Journal of Science 13 (2017): 165-169 Chicago Taşyurdu, Y , Dilmen, Z . "On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix". Celal Bayar University Journal of Science 13 (2017): 165-169 RIS TY - JOUR T1 - On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix AU - Yasemin Taşyurdu , Zülküf Dilmen Y1 - 2017 PY - 2017 N1 - doi: 10.18466/cbayarfbe.302663 DO - 10.18466/cbayarfbe.302663 T2 - Celal Bayar University Journal of Science JF - Journal JO - JOR SP - 165 EP - 169 VL - 13 IS - 1 SN - 1305-130X-1305-1385 M3 - doi: 10.18466/cbayarfbe.302663 UR - https://doi.org/10.18466/cbayarfbe.302663 Y2 - 2019 ER - EndNote %0 Celal Bayar University Journal of Science On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix %A Yasemin Taşyurdu , Zülküf Dilmen %T On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix %D 2017 %J Celal Bayar University Journal of Science %P 1305-130X-1305-1385 %V 13 %N 1 %R doi: 10.18466/cbayarfbe.302663 %U 10.18466/cbayarfbe.302663 ISNAD Taşyurdu, Yasemin , Dilmen, Zülküf . "On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix". Celal Bayar University Journal of Science 13 / 1 (March 2017): 165-169. https://doi.org/10.18466/cbayarfbe.302663