In this study, a matrix $R_{v}$ is defined, and two closed form expressions of the matrix $R_{v}^{n}$, for an integer $n\geq 1$, are evaluated by the matrix functions in matrix theory. These expressions satisfy a connection between the generalized Fibonacci and Lucas numbers with the Pascal matrices. Thus, two representations of the matrix $R_{v}^{n}$ and various forms of matrix $(R_{v}+q\triangle I)^{n}$ are studied in terms of the generalized Fibonacci and Lucas numbers and binomial coefficients. By modifying results of $2\times 2$ matrix representations given in the references of our study, we give various $3\times 3$ matrix representations of the generalized Fibonacci and Lucas sequences. Many combinatorial identities are derived as
applications.
generalized Fibonacci and Lucas sequences generalized Fibonacci and Lucas matrices Pascal matrices
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Yayımlanma Tarihi | 6 Ekim 2020 |
Yayımlandığı Sayı | Yıl 2020 Cilt: 49 Sayı: 5 |