Results 31 to 40 of about 94,026 (132)

On Leonardo numbers

, 2019
In this paper, we consider the sequence of Leonardo numbers and we present some properties involving this sequence, including the Binet formula, and the generating function. Furthermore, Cassini’s identity, Catalan’s identity and d’Ocagne’s identity for this sequence are given. Also some expressions of sums and products involving terms of this sequence
Paula Catarino, A. Borges
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A note on hybrid hyper Leonardo numbers

Turkish Journal of Mathematics
Summary: Recently, many studies have been devoted to extending particular sets of integers to other special sets, such as complex, dual, hyperbolic, and hybrid numbers. In this study, we define a new generalization of the Leonardo sequence consisting of the hybrid hyper-Leonardo numbers.
Elen Viviani Pereira Spreafico, Paula Catarino   +1 more
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Leonardo Numbers and their Bicomplex Extension

Nepal Journal of Mathematical Sciences
This paper introduces a new type of Leonardo numbers, referred to as bicomplex Leonardoi numbers. Also, some important relations, including the generating function, Binet's formula, D'Ocagne's identity, Cassini’s identity, and Catalan’s identity. Furthermore, we present the relationship between Lucas, Fibonacci, and Leonardo numbers.
Manoj K. Jaiswal, Narayan Prasad Pahari, Purushottam Parajuli   +2 more
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q-Leonardo Hyper Dual Numbers

, 2023
Murat Turan, Sıddıka Özkaldı Karakuş   +1 more
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Tri–Periodic Fibonacci Numbers and Tri–Periodic Leonardo Numbers

In this study, we explore the properties of tri-periodic Fibonacci and tri-periodic Leonardo number sequences. Then we derive generating function of these sequences and give Binet's formula for the tri-periodic Fibonacci sequence. Furthermore, we present Cassani's identity associated with tri-periodic Fibonacci sequnce.
Banu Yılmaz, Yüksel Soykan
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A Study on Dual Hyperbolic Generalised Leonardo Numbers

Asian Research Journal of Mathematics
In this study, we present a comprehensive formalization of dual hyperbolic generalized Leonardo numbers, systematically examining their structural properties and mathematical significance. The dual hyperbolic number system plays a crucial role in mathematical analysis, as its application to numerical sequences leads to the emergence of novel algebraic ...
Can Murat Dikmen
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Introduction to generalized Leonardo-Alwyn hybrid numbers [PDF]

11 ...
Gamaliel Cerda-Morales
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Pauli–Leonardo quaternions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this study, we define Pauli–Leonardo quaternions by taking the coefficients of the Pauli quaternions as Leonardo numbers. We give the recurrence relation, Binet formula, generating function, exponential generating function, some special equalities ...
Zehra İşbilir, Mahmut Akyiğit, Murat Tosun   +2 more
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A note on generalized Leonardo numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2019
A. G. Shannon
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Hybrid Quaternions of Leonardo

Trends in Computational and Applied Mathematics, 2022
In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented.
M. C. S. Mangueira, F. R. V. Alves, P. M. M. C. Catarino   +2 more
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