On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix
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.
___
- 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.