Leonardo and hyper-Leonardo numbers via Riordan arrays-Reference-Cited by-同舟云学术

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Leonardo and hyper-Leonardo numbers via Riordan arrays

Published:2024-03-25 Issue:3 Volume:76 Page:
ISSN:1027-3190
Container-title:Ukrains’kyi Matematychnyi Zhurnal
language:
Short-container-title:Ukr. Mat. Zhurn.

Author:

Alp Yasemin,Kocer E. Gokcen

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.

Publisher

SIGMA (Symmetry, Integrability and Geometry: Methods and Application)

Reference20 articles.

1. Y. Alp, E. G. Kocer, Some properties of Leonardo numbers, Konuralp J. Math., 9, № 1, 183–189 (2021).

2. M. Bahsi, I. Mezo, S. Solak, A symmetric algorithm for hyper-Fibonacci and hyper-Lucas numbers, Ann. Math. et Inform., 43, 19–27 (2014).

3. F. Y. Baran, N. Tuglu, $q$-Riordan representation, Linear Algebra and Appl., 525, 105–117 (2017).

4. P. Catarino, A. Borges, On Leonardo numbers, Acta Math. Univ. Comenian, 89, № 1, 75–86 (2019).

5. M. Cetin, C. Kizilates, F. Y. Baran, N. Tuglu, Some identities of harmonic and hyperharmonic Fibonacci numbers, Gazi Univ. J. Sci., 34, № 2, 493–504 (2021).

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