Leonardo and hyper-Leonardo numbers via Riordan arrays
UDC 511 A generalization of the Leonardo numbers is defined and called the hyper-Leonardo numbers. Infinite lower triangular matrices, whose elements are Leonardo and hyper-Leonardo numbers are considered. Then the $A$- and $Z$-sequences of these matrices are o...
Saved in:
| Date: | 2024 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2024
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7296 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512648704032768 |
|---|---|
| author | Alp, Yasemin Kocer, E. Gokcen Alp, Yasemin Kocer, E. Gokcen |
| author_facet | Alp, Yasemin Kocer, E. Gokcen Alp, Yasemin Kocer, E. Gokcen |
| author_sort | Alp, Yasemin |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:16Z |
| description | UDC 511
A generalization of the Leonardo numbers is defined and called the hyper-Leonardo numbers. Infinite lower triangular matrices, whose elements are Leonardo and hyper-Leonardo numbers are considered. Then the $A$- and $Z$-sequences of these matrices are obtained. Finally, the combinatorial identities between the hyper-Leonardo and Fibonacci numbers are obtained using the fundamental theorem of the Riordan arrays. |
| doi_str_mv | 10.3842/umzh.v45i3.7296 |
| first_indexed | 2026-03-24T03:32:08Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7296 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:08Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-72962024-06-19T00:35:16Z Leonardo and hyper-Leonardo numbers via Riordan arrays Leonardo and hyper-Leonardo numbers via Riordan arrays Alp, Yasemin Kocer, E. Gokcen Alp, Yasemin Kocer, E. Gokcen Fibonacci numbers Leonardo numbers Riordan arrays UDC 511 A generalization of the Leonardo numbers is defined and called the hyper-Leonardo numbers. Infinite lower triangular matrices, whose elements are Leonardo and hyper-Leonardo numbers are considered. Then the $A$- and $Z$-sequences of these matrices are obtained. Finally, the combinatorial identities between the hyper-Leonardo and Fibonacci numbers are obtained using the fundamental theorem of the Riordan arrays. УДК 511 Числа та гіперчисла Леонардо в термінах масивів Ріордана Визначено узагальнення чисел Леонардо, яке називається гіперчислами Леонардо. Розглянуто нескінченні нижчі трикутні матриці, елементами  яких є числа Леонардо та гіперчисла Леонардо. Крім того, отримано $A$- та $Z$-послідовності цих матриць. Насамкінець за допомогою фундаментальної теореми про масиви Ріордана отримано комбінаторні тотожності між  гіперчислами Леонардо та числами Фібоначчі.  Institute of Mathematics, NAS of Ukraine 2024-03-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7296 10.3842/umzh.v45i3.7296 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 3 (2024); 326–340 Український математичний журнал; Том 76 № 3 (2024); 326–340 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7296/9850 Copyright (c) 2024 Yasemin ALP, E.Gokcen KOCER |
| spellingShingle | Alp, Yasemin Kocer, E. Gokcen Alp, Yasemin Kocer, E. Gokcen Leonardo and hyper-Leonardo numbers via Riordan arrays |
| title | Leonardo and hyper-Leonardo numbers via Riordan arrays |
| title_alt | Leonardo and hyper-Leonardo numbers via Riordan arrays |
| title_full | Leonardo and hyper-Leonardo numbers via Riordan arrays |
| title_fullStr | Leonardo and hyper-Leonardo numbers via Riordan arrays |
| title_full_unstemmed | Leonardo and hyper-Leonardo numbers via Riordan arrays |
| title_short | Leonardo and hyper-Leonardo numbers via Riordan arrays |
| title_sort | leonardo and hyper-leonardo numbers via riordan arrays |
| topic_facet | Fibonacci numbers Leonardo numbers Riordan arrays |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7296 |
| work_keys_str_mv | AT alpyasemin leonardoandhyperleonardonumbersviariordanarrays AT koceregokcen leonardoandhyperleonardonumbersviariordanarrays AT alpyasemin leonardoandhyperleonardonumbersviariordanarrays AT koceregokcen leonardoandhyperleonardonumbersviariordanarrays |