Ordered Leonardo Quadruple Numbers
In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which we call ordered Leonardo quadruple numbers. We determine the properties of ordered Leonardo quadruple numbers including relations with Leonardo, Fibonacci, and Lucas numbers. Symmetric and antisymmetric p...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/1/149 |
| _version_ | 1797436858143080448 |
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| author | Semra Kaya Nurkan İlkay Arslan Güven |
| author_facet | Semra Kaya Nurkan İlkay Arslan Güven |
| author_sort | Semra Kaya Nurkan |
| collection | DOAJ |
| description | In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which we call ordered Leonardo quadruple numbers. We determine the properties of ordered Leonardo quadruple numbers including relations with Leonardo, Fibonacci, and Lucas numbers. Symmetric and antisymmetric properties of Fibonacci numbers are used in the proofs. We attain some well-known identities, the Binet formula, and a generating function for these numbers. Finally, we provide illustrations of the identities. |
| first_indexed | 2024-03-09T11:08:39Z |
| format | Article |
| id | doaj.art-f5b7590082f844f5b725fe30469a8df7 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T11:08:39Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f5b7590082f844f5b725fe30469a8df72023-12-01T00:52:36ZengMDPI AGSymmetry2073-89942023-01-0115114910.3390/sym15010149Ordered Leonardo Quadruple NumbersSemra Kaya Nurkan0İlkay Arslan Güven1Department of Mathematics, Faculty of Arts and Science, Usak University, TR-64200 Uşak, TurkeyDepartment of Mathematics, Faculty of Arts and Science, Gaziantep University, TR-27310 Gaziantep, TurkeyIn this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which we call ordered Leonardo quadruple numbers. We determine the properties of ordered Leonardo quadruple numbers including relations with Leonardo, Fibonacci, and Lucas numbers. Symmetric and antisymmetric properties of Fibonacci numbers are used in the proofs. We attain some well-known identities, the Binet formula, and a generating function for these numbers. Finally, we provide illustrations of the identities.https://www.mdpi.com/2073-8994/15/1/149Fibonacci quaternionsLeonardo numbersquadruple numbers |
| spellingShingle | Semra Kaya Nurkan İlkay Arslan Güven Ordered Leonardo Quadruple Numbers Symmetry Fibonacci quaternions Leonardo numbers quadruple numbers |
| title | Ordered Leonardo Quadruple Numbers |
| title_full | Ordered Leonardo Quadruple Numbers |
| title_fullStr | Ordered Leonardo Quadruple Numbers |
| title_full_unstemmed | Ordered Leonardo Quadruple Numbers |
| title_short | Ordered Leonardo Quadruple Numbers |
| title_sort | ordered leonardo quadruple numbers |
| topic | Fibonacci quaternions Leonardo numbers quadruple numbers |
| url | https://www.mdpi.com/2073-8994/15/1/149 |
| work_keys_str_mv | AT semrakayanurkan orderedleonardoquadruplenumbers AT ilkayarslanguven orderedleonardoquadruplenumbers |