A second-order difference equation with sign-alternating coefficients

Kuwait Journal of Science

article

Carlos Fonseca¹  Can Kizilates²  Nazlihan Terzioglu² 

[1] Kuwait College of Science and Technology;Dept. of Mathematics, Zonguldak B¨ulent Ecevit University

关键词: Chebyshev polynomials of the second kind;    difference equations;    Fibonacci numbers;    integer sequences;    tridiagonal matrices;   

DOI  :  10.48129/kjs.20425

学科分类：社会科学、人文和艺术（综合）

来源: Kuwait University * Academic Publication Council

【 摘 要 】

We provide an explicit solution for the terms of the sequence $(x_{n,k})$ defined by $$x_{n,k}= x_{n-1,k} - (-1)^{\lfloor (n-2)/k\rfloor} x_{n-2,k}\, ,$$ for $n\geqslant 3$, setting $x_{1,k}=1$ and $x_{2,k}=0$. Several particular examples are considered.

【 授权许可】

Unknown