Leonardo and hyper-Leonardo numbers via Riordan arrays

Yasemin Alp; E. Gokcen Kocer

doi:10.3842/umzh.v45i3.7296

Yasemin Alp Department of Education of Mathematics and Science, Faculty of Education, Selcuk University, Konya, Turkey
E. Gokcen Kocer Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, Konya, Turkey

DOI: https://doi.org/10.3842/umzh.v45i3.7296

Keywords: Fibonacci numbers, Leonardo numbers, Riordan arrays

Abstract

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.

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