Leonardo and Hyper-Leonardo Numbers Via Riordan Arrays

IF 0.5 4区数学 Q3 MATHEMATICS

Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI:10.1007/s11253-024-02325-8

Yasemin Alp, E. Gokcen Kocer

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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通过瑞尔丹数组计算莱昂纳多和超莱昂纳多数

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ukrainian Mathematical Journal MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

107

审稿时长

4-8 weeks

期刊介绍： Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries. Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.