Results 1 to 10 of about 104,771 (272)

Notes on generalized and extended Leonardo numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
This paper both extends and generalizes recently published properties which have been developed by many authors for elements of the Leonardo sequence in the context of second-order recursive sequences.
Anthony G. Shannon, Peter J.-S. Shiue, Shen C. Huang   +2 more
doaj   +2 more sources

On Leonardo Pisano Hybrinomials

Mathematics, 2021
A generalization of complex, dual, and hyperbolic numbers has recently been defined as hybrid numbers. In this study, using the Leonardo Pisano numbers and hybrid numbers we investigate Leonardo Pisano polynomials and hybrinomials.
Ferhat Kürüz, Ali Dağdeviren, Paula Catarino   +2 more
exaly   +3 more sources

On Gaussian Leonardo numbers [PDF]

Contributions to Mathematics, 2023
Dursun Taşcı
doaj   +2 more sources

On Hybrid Numbers with Gaussian Leonardo Coefficients

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   +2 more sources

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

Contributions to Mathematics
Summary: In this paper, we introduce hyper-Leonardo \(p\)-numbers, which generalize ``hyper-Leonardo numbers''. We establish their various combinatorial properties, including recurrence relations, summation formulas, and the generating function. We also compute Euclidean norms and obtain bounds for spectral norms of different forms of \(k\)-circulant ...
Nassima Belaggoun, Hacène Belbachir
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

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   +3 more sources

A Note on the Fuzzy Leonardo Numbers

Transactions on Fuzzy Sets and Systems
In this work, we define a new sequence denominated by fuzzy Leonardo numbers. Some algebraic properties of this new sequence are studied and several identities are established.
Elen Viviani Pereira Spreafico, Eudes Antonio Costa, Paula Maria Machado Cruz Catarino   +2 more
doaj   +2 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

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

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   +1 more source