{"title":"Leonardo and Hyper-Leonardo Numbers Via Riordan Arrays","authors":"Yasemin Alp, E. Gokcen Kocer","doi":"10.1007/s11253-024-02325-8","DOIUrl":null,"url":null,"abstract":"<p>A generalization of the Leonardo numbers is defined and called hyper-Leonardo numbers. Infinite lowertriangular matrices whose elements are Leonardo and hyper-Leonardo numbers are considered. Then the <i>A</i>- and <i>Z</i>-sequences of these matrices are obtained. Finally, the combinatorial identities between the hyper-Leonardo and Fibonacci numbers are deduced by using the fundamental theorem on Riordan arrays.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02325-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A generalization of the Leonardo numbers is defined and called hyper-Leonardo numbers. Infinite lowertriangular 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 deduced by using the fundamental theorem on Riordan arrays.
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