Open AccessOn generalized K-Fibonacci sequence by two-cross-two matrix
Author(s) -
Arfat Ahmad Wani,
G. P. S. Rathore,
Kiran Sisodiya
Publication year - 2016
Publication title -
global journal of mathematical analysis
Language(s) - English
Resource type - Journals
ISSN - 2307-9002
DOI - 10.14419/gjma.v5i1.6949
Subject(s) - fibonacci number , sequence (biology) , matrix (chemical analysis) , mathematics , fibonacci polynomials , combinatorics , lucas number , identity matrix , pisano period , representation (politics) , physics , eigenvalues and eigenvectors , chemistry , quantum mechanics , politics , political science , law , orthogonal polynomials , difference polynomials , biochemistry , chromatography
In this study we define a new generalized k-Fibonacci sequence associated with its two cross two matrix called generating matrix. After use the matrix representation we find many interesting properties such as nth power of the matrix, Cassini's Identity of generalized k-Fibonacci sequence as well as Binet's formula for generalized k-Fibonacci sequence by the method of matrix diagonalization.