Two Generalizations of Dual-Hyperbolic Balancing Numbers
In this paper, we study two generalizations of dual-hyperbolic balancing numbers: dual-hyperbolic Horadam numbers and dual-hyperbolic <i>k</i>-balancing numbers. We give Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity for them.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-11-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/11/1866 |
| _version_ | 1797547973108826112 |
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| author | Dorota Bród Anetta Szynal-Liana Iwona Włoch |
| author_facet | Dorota Bród Anetta Szynal-Liana Iwona Włoch |
| author_sort | Dorota Bród |
| collection | DOAJ |
| description | In this paper, we study two generalizations of dual-hyperbolic balancing numbers: dual-hyperbolic Horadam numbers and dual-hyperbolic <i>k</i>-balancing numbers. We give Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity for them. |
| first_indexed | 2024-03-10T14:52:45Z |
| format | Article |
| id | doaj.art-4c390f928dc64dbcaf95d16d0544e07a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:52:45Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4c390f928dc64dbcaf95d16d0544e07a2023-11-20T20:51:38ZengMDPI AGSymmetry2073-89942020-11-011211186610.3390/sym12111866Two Generalizations of Dual-Hyperbolic Balancing NumbersDorota Bród0Anetta Szynal-Liana1Iwona Włoch2The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, PolandThe Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, PolandThe Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, PolandIn this paper, we study two generalizations of dual-hyperbolic balancing numbers: dual-hyperbolic Horadam numbers and dual-hyperbolic <i>k</i>-balancing numbers. We give Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity for them.https://www.mdpi.com/2073-8994/12/11/1866balancing numbersDiophantine equationdual-hyperbolic numbersBinet formulaCatalan’s identity |
| spellingShingle | Dorota Bród Anetta Szynal-Liana Iwona Włoch Two Generalizations of Dual-Hyperbolic Balancing Numbers Symmetry balancing numbers Diophantine equation dual-hyperbolic numbers Binet formula Catalan’s identity |
| title | Two Generalizations of Dual-Hyperbolic Balancing Numbers |
| title_full | Two Generalizations of Dual-Hyperbolic Balancing Numbers |
| title_fullStr | Two Generalizations of Dual-Hyperbolic Balancing Numbers |
| title_full_unstemmed | Two Generalizations of Dual-Hyperbolic Balancing Numbers |
| title_short | Two Generalizations of Dual-Hyperbolic Balancing Numbers |
| title_sort | two generalizations of dual hyperbolic balancing numbers |
| topic | balancing numbers Diophantine equation dual-hyperbolic numbers Binet formula Catalan’s identity |
| url | https://www.mdpi.com/2073-8994/12/11/1866 |
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