Results 1 to 10 of about 102,319 (175)

Dual Leonardo numbers

AIMS Mathematics, 2023
This paper introduced the concept of dual Leonardo numbers to generalize the earlier studies in harmony and establish key formulas, including the Binet formula and the generating function. Both were employed to obtain specific elements from the sequence.
Adnan Karataş
doaj   +4 more sources

On Hybrid Numbers with Gaussian Leonardo Coefficients [PDF]

Mathematics, 2023
We consider the Gaussian Leonardo numbers and investigate some of their amazing characteristic properties, including their generating function, the associated Binet formula and Cassini identity, and their matrix representation. Then, we define the hybrid
Nagihan Kara, Fatih Yilmaz
doaj   +3 more sources

A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields [PDF]

Mathematics, 2023
In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q-Leonardo hybrid numbers.
Elif Tan, Diana Savin, Semih Yılmaz
doaj   +3 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   +4 more sources

On Gaussian Leonardo numbers [PDF]

Contributions to Mathematics, 2023
Dursun Taşcı
doaj   +3 more sources

Some Properties of the Generalized Leonardo Numbers

Journal of New Theory
In this study, various properties of the generalized Leonardo numbers, which are one of the generalizations of Leonardo numbers, have been investigated. Additionally, some identities among the generalized Leonardo numbers have been obtained. Furthermore,
Yasemin Alp
doaj   +4 more sources

Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers

Axioms
This article introduces new polynomials that extend the standard Leonardo numbers, generalizing Fibonacci and Lucas polynomials. A new power form representation is developed for these polynomials, which is crucial for deriving further formulas.
Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori, Abdulrahim A. Alluhaybi, Amr Kamel Amin   +3 more
doaj   +3 more sources

On complex Leonardo numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2022
In this study, we introduce the complex Leonardo numbers and give some of their properties including Binet formula, generating function, Cassini and d’Ocagne’s identities. Also, we calculate summation formulas for complex Leonardo numbers involving complex Fibonacci and Lucas numbers.
Adnan Karataş
openaire   +4 more sources

On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal [PDF]

Journal of Function Spaces, 2022
In the present study, we have constructed new Banach sequence spaces ℓpL,c0L,cL, and ℓ∞L, where L=lv,k is a regular matrix defined by lv,k=lk/lv+2−v+2, 0≤k≤v,0, k>v, for all v,k=0,1,2,⋯, where l=lk is a sequence of Leonardo numbers.
Taja Yaying, Bipan Hazarika, O. M. Kalthum S. K. Mohamed, Awad A. Bakery   +3 more
doaj   +2 more sources

Hyper-Leonardo p-numbers and associated norms [PDF]

Contributions to Mathematics
Nassima Belaggoun, Hacène Belbachir
doaj   +3 more sources