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

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

References

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