A Two-by-Two matrix representation of a generalized Fibonacci sequence

Year 2018, Volume: 47 Issue: 3, 637 - 648, 01.06.2018

Arfat Ahmad Wani , G. P. S. Rathore V. H. Badshah Kiran Sisodiya

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

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