{"title":"通过瑞尔丹数组计算莱昂纳多和超莱昂纳多数","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":"{\"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}","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
摘要
莱昂纳多数的广义定义被称为超莱昂纳多数。我们考虑了元素为莱昂纳多数和超莱昂纳多数的无穷低三角矩阵。然后得到这些矩阵的 A 序列和 Z 序列。最后，利用瑞尔丹数组基本定理推导出超莱昂纳多数和斐波那契数之间的组合同构。
Leonardo and Hyper-Leonardo Numbers Via Riordan Arrays
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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