- Hacettepe Journal of Mathematics and Statistics
- Vol: 47 Issue: 3
- A Two-by-Two matrix representation of a generalized Fibonacci sequence
A Two-by-Two matrix representation of a generalized Fibonacci sequence
Authors : Arfat Ahmad Wani, G. P. S. Rathore, V. H. Badshah, Kiran Sisodiya
Pages : 637-648
View : 10 | Download : 6
Publication Date : 2018-06-01
Article Type : Research
Abstract :The Fibonacci sequence is a well-known example of second order recurrence sequence, which belongs to a particular class of recursive sequences. In this article, other generalized Fibonacci sequence is introduced and defined by $ H_{k,n+1}=2H_{k,n}+kH_{k,n-1},~n\geq1,~H_{k,0}=2,~H_{k,1}=1$ and $k$ is the positive real number. Also $n^{th}$ power of the generating matrix for this generalized Fibonacci sequence is established and some basic properties of this sequence are obtained by matrix methods.Keywords : Fibonacci Sequence, Generalized Fibonacci Sequences and Matrix Methods