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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-03-01
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| Series: | Kuwait Journal of Science |
| Online Access: | https://journalskuwait.org/kjs/index.php/KJS/article/view/20425 |
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| _version_ | 1849744752864395264 |
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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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| format | Article |
| id | doaj-art-115e167f90594d0c8e5759f7b45668d9 |
| institution | DOAJ |
| issn | 2307-4108 2307-4116 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Elsevier |
| record_format | Article |
| 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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