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

被引：15
|
作者：
Tan, Elif [1 ]
Leung, Ho-Hon [2 ]
机构：
[1] Ankara Univ, Fac Sci, Dept Math, Ankara, Turkey
[2] UAEU, Dept Math Sci, Al Ain, U Arab Emirates
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期
关键词：
Horadam sequence; Bi-periodic Fibonacci sequence; Matrix method; 11B39; 05A15; IDENTITIES;
D O I：
10.1186/s13662-020-2507-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a generalization of Horadam sequence {wn} which is defined by the recurrence relation wn=chi (n)wn-1+cwn-2, where chi (n)=a if n is even, chi (n)=b if n is odd with arbitrary initial conditions w0, w1 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 {un} and {vn}, respectively. The main purpose of this study is to derive some basic properties of the sequences {un}, {vn} and {wn} by using a matrix approach.
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页数：11
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