A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila
2021-12-01
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| Series: | Journal of Innovative Applied Mathematics and Computational Sciences |
| Subjects: | |
| Online Access: | http://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/7 |
| _version_ | 1828345536743211008 |
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| author | Yüksel Soykan Erkan Taşdemir Can Murat Dikmen |
| author_facet | Yüksel Soykan Erkan Taşdemir Can Murat Dikmen |
| author_sort | Yüksel Soykan |
| collection | DOAJ |
| description |
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are
presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.
|
| first_indexed | 2024-04-14T00:13:34Z |
| format | Article |
| id | doaj.art-ab9847d49cc941e9b6d5803615a76700 |
| institution | Directory Open Access Journal |
| issn | 2773-4196 |
| language | English |
| last_indexed | 2024-04-14T00:13:34Z |
| publishDate | 2021-12-01 |
| publisher | Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila |
| record_format | Article |
| series | Journal of Innovative Applied Mathematics and Computational Sciences |
| spelling | doaj.art-ab9847d49cc941e9b6d5803615a767002022-12-22T02:23:15ZengInstitute of Sciences and Technology, University Center Abdelhafid Boussouf, MilaJournal of Innovative Applied Mathematics and Computational Sciences2773-41962021-12-0111A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$Yüksel Soykan0Erkan Taşdemir1Can Murat Dikmen2ZONGULDAK BÜLENT ECEVIT UNIVERSITYKırklareli UniversityZONGULDAK BÜLENT ECEVIT UNIVERSITY In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers. http://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/7Balancing numbersmodified Lucas-balancing numbersLucas-balancing numberssum formulas |
| spellingShingle | Yüksel Soykan Erkan Taşdemir Can Murat Dikmen A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ Journal of Innovative Applied Mathematics and Computational Sciences Balancing numbers modified Lucas-balancing numbers Lucas-balancing numbers sum formulas |
| title | A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ |
| title_full | A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ |
| title_fullStr | A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ |
| title_full_unstemmed | A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ |
| title_short | A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ |
| title_sort | study on the sum of the squares of generalized balancing numbers the sum formula sum k 0 n x k w mk j 2 |
| topic | Balancing numbers modified Lucas-balancing numbers Lucas-balancing numbers sum formulas |
| url | http://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/7 |
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