On the Jacobsthal-Lucas Numbers by Matrix Method
نویسندگان
چکیده
In this study, we define the Jacobsthal Lucas E-matrix and R-matrix alike to the Fibonacci Q-matrix. Using this matrix represantation we have found some equalities and Binet-like formula for the Jacobsthal and Jacobsthal-Lucas numbers.
منابع مشابه
On the sum of Pell and Jacobsthal numbers by matrix method
In this paper, we define two $n$-square upper Hessenberg matrices one of which corresponds to the adjacency matrix of a directed pseudo graph. We investigate relations between permanents and determinants of these upper Hessenberg matrices, and sum formulas of the well-known Pell and Jacobsthal sequences. Finally, we present two Maple 13 procedures in order to calculate permanents of t...
متن کاملSome Bounds for the Norms of Circulant Matrices with the k-Jacobsthal and k-Jacobsthal Lucas Numbers
Abstract In this paper we investigate upper and lower bounds of the norms of the circulant matrices whose elements are k−Jacobsthal numbers and k−Jacobsthal Lucas numbers.
متن کاملOn Some Identities of k-Jacobsthal-Lucas Numbers
In this paper we present the sequence of the k-Jacobsthal-Lucas numbers that generalizes the Jacobsthal-Lucas sequence introduced by Horadam in 1988. For this new sequence we establish an explicit formula for the term of order n, the well-known Binet’s formula, Catalan’s and d’Ocagne’s Identities and a generating function. Mathematics Subject Classification 2010: 11B37, 11B83
متن کاملSome Generalizations of the Jacobsthal Numbers
The main object of this paper is to introduce and investigate some properties and relations involving sequences of numbers Fn,m(r), for m = 2, 3, 4, and r is some real number. These sequences are generalizations of the Jacobsthal and Jacobsthal Lucas numbers.
متن کاملGeneralized Bivariate Lucas p-Polynomials and Hessenberg Matrices
In this paper, we give some determinantal and permanental representations of generalized bivariate Lucas p-polynomials by using various Hessenberg matrices. The results that we obtained are important since generalized bivariate Lucas p-polynomials are general forms of, for example, bivariate Jacobsthal-Lucas, bivariate Pell-Lucas ppolynomials, Chebyshev polynomials of the first kind, Jacobsthal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008