Results 21 to 30 of about 1,582,486 (262)

Generalized Horadam-Leonardo Numbers and Polynomials

Asian Journal of Advanced Research and Reports, 2023
In this study, we define and investigate some linear third order polynomials called the generalized Horadam-Leonardo polynomials (with its two special cases, namely), (r, s)-Horadam-Leonardo and (r, s)-Horadam-Leonardo-Lucas polynomials. We give Binet’s formulas, generating functions, Simson formulas, and the sumformulas for these polynomial sequences.
Yüksel Soykan, Soykan, Yüksel
openaire   +2 more sources

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
Catarino, Paula, Borges, Anabela
core   +3 more sources

A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Journal of Mathematics
In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1.
Hasan Gökbaş
exaly   +2 more sources

Some results on geometric circulant matrices involving the Leonardo numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In this study, by the motivation of the papers in the literature, we construct a special geometric circulant matrix Leᵣ* whose entries are the Leonardo numbers. Then, we investigate some linear algebraic properties of these matrices.
Samet Arpacı, Fatih Yılmaz
doaj   +3 more sources

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   +1 more source

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
openaire   +3 more sources

Generalized Leonardo Numbers [PDF]

, 2021
In this paper, we investigate the generalized Leonardo sequences and we deal with, in detail, three special cases, namely, modified Leonardo, Leonardo-Lucas and Leonardo sequences.
Soykan, Yüksel
core   +2 more sources

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