A second-order difference equation with sign-alternating coefficients

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.

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Bibliographic Details
Main Authors: Prof.Carlos Fonseca, Can Kizilates, Nazlihan Terzioglu
Format: Article
Language:English
Published: Elsevier 2023-03-01
Series:Kuwait Journal of Science
Online Access:https://journalskuwait.org/kjs/index.php/KJS/article/view/20425
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author Prof.Carlos Fonseca
Can Kizilates
Nazlihan Terzioglu
author_facet Prof.Carlos Fonseca
Can Kizilates
Nazlihan Terzioglu
author_sort Prof.Carlos Fonseca
collection DOAJ
description 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.
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2307-4116
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publishDate 2023-03-01
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series Kuwait Journal of Science
spelling doaj-art-115e167f90594d0c8e5759f7b45668d92025-08-20T03:09:45ZengElsevierKuwait Journal of Science2307-41082307-41162023-03-01502A10.48129/kjs.20425A second-order difference equation with sign-alternating coefficientsProf.Carlos Fonseca0Can Kizilates1Nazlihan Terzioglu2Kuwait College of Science and Technology, P.O. Box 27235, Safat 13133, KuwaitDept. of Mathematics, Zonguldak B¨ulent Ecevit University, Zonguldak, 67100, TurkeyDept. of Mathematics, Zonguldak B¨ulent Ecevit University, Zonguldak, 67100, Turkey 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. https://journalskuwait.org/kjs/index.php/KJS/article/view/20425
spellingShingle Prof.Carlos Fonseca
Can Kizilates
Nazlihan Terzioglu
A second-order difference equation with sign-alternating coefficients
Kuwait Journal of Science
title A second-order difference equation with sign-alternating coefficients
title_full A second-order difference equation with sign-alternating coefficients
title_fullStr A second-order difference equation with sign-alternating coefficients
title_full_unstemmed A second-order difference equation with sign-alternating coefficients
title_short A second-order difference equation with sign-alternating coefficients
title_sort second order difference equation with sign alternating coefficients
url https://journalskuwait.org/kjs/index.php/KJS/article/view/20425
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