A Two-by-Two Matrix Representation of a Generalized Fibonacci Sequence | Zendy

Arfat Ahmad Wani | Zendy

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A Two-by-Two Matrix Representation of a Generalized Fibonacci Sequence

Author(s) -

Arfat Ahmad Wani

Publication year - 2017

Publication title -

hacettepe journal of mathematics and statistics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.312

H-Index - 26

ISSN - 1303-5010

DOI - 10.15672/hjms.2017.477

Subject(s) - fibonacci number , mathematics , sequence (biology) , representation (politics) , combinatorics , matrix (chemical analysis) , algebra over a field , pure mathematics , genetics , materials science , politics , political science , law , composite material , biology

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.

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