Bi-periodic r-Fibonacci sequence and bi-periodic r-Lucas sequence of type s
نویسندگان
چکیده
In the present paper, for a positive integer $r$, we study bi-periodic $r$-Fibonacci sequence and its family of companion sequences, $r$-Lucas type $s$ with $1 \leq s r$, which extend classical Fibonacci Lucas sequences. Afterwards, establish link between Furthermore, give their properties as linear recurrence relations, generating functions, explicit formulas Binet forms.
منابع مشابه
A Q-analog of the Bi-periodic Lucas Sequence
In this paper, we introduce a q-analog of the bi-periodic Lucas sequence, called as the q-bi-periodic Lucas sequence, and give some identities related to the q-bi-periodic Fibonacci and Lucas sequences. Also, we give a matrix representation for the q-bi-periodic Fibonacci sequence which allow us to obtain several properties of this sequence in a simple way. Moreover, by using the explicit formu...
متن کاملCorrection to: On the spectral norms of r-circulant matrices with the bi-periodic Fibonacci and Lucas numbers
*Correspondence: [email protected] Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Nevşehir, Turkey 1 Correction In the publication of this article [1], there are a few errors. (1) Page 4, line 4: The statement 1 (ab)m+1 [α 2m+1 + β2m+1 – (–1)m] – 2 should instead read: 1 (ab)m+1 [α 2m+1 + β2m+1] + (–1)m – 2. (2) Page 4, line 6: The statement ( 1 a )lmlm+1 = 1 (ab)m+1 [α ...
متن کاملGenerating matrix of the bi-periodic Lucas numbers
In this paper, firstly, we introduce the Ql-Generating matrix for the bi-periodic Lucas numbers. Then, by taking into account this matrix representation, we obtain some properties for the bi-periodic Fibonacci and Lucas numbers.
متن کاملThe K-periodic Fibonacci Sequence and an Extended Binet’s Formula
It is well-known that a continued fraction is periodic if and only if it is the representation of a quadratic irrational α. In this paper, we consider the family of sequences obtained from the recurrence relation generated by the numerators of the convergents of these numbers α. These sequences are generalizations of most of the Fibonacci-like sequences, such as the Fibonacci sequence itself, r...
متن کاملThree-dimensional Gaussian Beam Scattering from a Periodic Sequence of Bi-isotropic and Material Layers
The three-dimensional Gaussian beam scattering from the bounded periodic sequence of one-to-one composed isotropic magnetodielectric and bi-isotropic layers are investigated. The beam field is represented by an angular continuous spectrum of plane wave. The problem of the partial plane wave diffraction on the structure is solved using the circuit theory and the transfer matrix methods. It is fo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hacettepe journal of mathematics and statistics
سال: 2022
ISSN: ['1303-5010']
DOI: https://doi.org/10.15672/hujms.825908