Results 1 to 10 of about 13,753 (265)

Special Cases of Generalized Leonardo Numbers : Modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo Numbers

Earthline Journal of Mathematical Sciences, 2022
In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences.
Yüksel Soykan
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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
doaj   +2 more sources

On Dual Quaternions with $k-$Generalized Leonardo Components

Journal of New Theory, 2023
In this paper, we define a one-parameter generalization of Leonardo dual quaternions, namely $k-$generalized Leonardo-like dual quaternions. We introduce the properties of $k$-generalized Leonardo-like dual quaternions, including relations with Leonardo,
Gülsüm Yeliz Saçlı, Çiğdem Zeynep Yılmaz   +1 more
doaj   +2 more sources

Pell Leonardo numbers and their matrix representations

Journal of New Results in Science
In this study, we investigate Pell numbers and Leonardo numbers and describe a new third-order number sequence entitled Pell Leonardo numbers. We then construct some identities, including the Binet formula, generating function, exponential generating ...
Çağla Çelemoğlu
doaj   +3 more sources

A new generalization of Leonardo hybrid numbers with q-integers

Indian Journal of Pure and Applied Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hayrullah Özimamoğlu
exaly   +3 more sources

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
doaj   +1 more source

On the Generalized Leonardo Numbers

, 2022
See the abstract in the attached pdf.
Kuhapatanakul, Kantaphon, Chobsorn, Juthamas   +1 more
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The Generalization of Gaussians and Leonardo’s Octonions

Annales Mathematicae Silesianae, 2023
In order to explore the Leonardo sequence, the process of complex-ification of this sequence is carried out in this work. With this, the Gaussian and octonion numbers of the Leonardo sequence are presented.
Vieira Renata Passos Machado, dos Santos Mangueira Milena Carolina, Alves Francisco Régis Vieira, Catarino Paula Maria Machado Cruz   +3 more
doaj   +1 more source

On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions

Journal of New Theory, 2023
In this paper, we present a new definition, referred to as the Francois sequence, related to the Lucas-like form of the Leonardo sequence. We also introduce the hyperbolic Leonardo and hyperbolic Francois quaternions.
Paula Maria Machado Cruz Catarino, Orhan Dışkaya, Hamza Menken   +2 more
doaj   +1 more source

GAUSSIAN LEONARDO POLYNOMIALS AND APPLICATIONS OF LEONARDO NUMBERS TO CODING THEORY

Journal of Science and Arts, 2023
In this paper, we firstly introduce the Gaussian Leonardo polynomial sequences {GLe_n (x)}_(n=0)^∞ and we obtain Binet's formula, generating function of this sequence. Moreover, we define the matrix Gl(x) in the form of 3 x 3. Finally, we study on the coding and decoding applications of the Leonardo number by using the Leonardo matrix P.
SELİME BEYZA ÖZÇEVİK, ABDULLAH DERTLİ   +1 more
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