Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences

Advances in Difference Equations

article

Tan, Elif¹  Leung, Ho-Hon² 

[1] Department of Mathematics, Faculty of Science, Ankara University;Department of Mathematical Sciences, United Arab Emirates

关键词: Horadam sequence;    Bi-periodic Fibonacci sequence;    Matrix method;   

DOI  :  10.1186/s13662-020-2507-4

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we consider a generalization of Horadam sequence $\{ w_{n} \} $ which is defined by the recurrence relation $w_{n}=\chi ( n ) w_{n-1}+cw_{n-2}$, where $\chi ( n ) =a$ if n is even, $\chi ( n ) =b$ if n is odd with arbitrary initial conditions $w_{0}$, $w_{1}$ and nonzero real numbers a, b and c. As a special case, by taking the initial conditions 0, 1 and 2, b we define the sequences $\{ u_{n} \} $ and $\{ v_{n} \} $, respectively. The main purpose of this study is to derive some basic properties of the sequences $\{ u _{n} \} $, $\{ v_{n} \} $ and $\{ w_{n} \} $ by using a matrix approach.

【 授权许可】

CC BY