Results 251 to 260 of about 217,165 (287)
Some of the next articles are maybe not open access.
Some new families of generalized \(k\)-Leonardo and Gaussian Leonardo numbers
2023Based on the authors abstract, this paper, introduces a new family of the generalized \(k\)-Leonardo numbers and study their properties. The authors investigate the Gaussian Leonardo numbers and associated new families of these Gaussian forms. They also obtain combinatorial identities like Binet formula, Cassini's identity, partial sum, etc.
Prasad, Kalika +3 more
openaire +2 more sources
2022
In literature until today, many authors have studied special sequences in different number systems. In this paper, using the Leonardo numbers, we introduce the bicomplex Leonardo numbers. Also, we give some algebraic properties of bicomplex Leonardo numbers such as recurrence relation, generating function, Binet’s formula, D’Ocagne’s identity, Cassini ...
openaire +1 more source
In literature until today, many authors have studied special sequences in different number systems. In this paper, using the Leonardo numbers, we introduce the bicomplex Leonardo numbers. Also, we give some algebraic properties of bicomplex Leonardo numbers such as recurrence relation, generating function, Binet’s formula, D’Ocagne’s identity, Cassini ...
openaire +1 more source
Common terms of Leonardo and Jacobsthal numbers
Rendiconti del Circolo Matematico di Palermo Series 2, 2023As a particular case of the Lucas sequences of the first kind, the sequence of Jacobsthal numbers \( \{J_m\}_{m\ge 0} \) is defined by the linear recurrence relation: \( J_0=0 \), \( J_1=1 \), and \( J_{m}=J_{m-1}+2J_{m-2} \) for all \( m\ge 2 \).
Bensella, Hayat, Behloul, Djilali
openaire +2 more sources
Logic Journal of the IGPL
Abstract This note covers some of the history of Leonardo numbers. We retrieve some of the most recent results on this sequence, as well as some relevant historical interconnections. In the end, we also provide some conjectures and open problems for some of its extensions involving the modular periodicity.
Carlos M da Fonseca +3 more
openaire +2 more sources
Abstract This note covers some of the history of Leonardo numbers. We retrieve some of the most recent results on this sequence, as well as some relevant historical interconnections. In the end, we also provide some conjectures and open problems for some of its extensions involving the modular periodicity.
Carlos M da Fonseca +3 more
openaire +2 more sources
Combinatorial Insights into Leonardo \(p\)-Numbers and Lucas-Leonardo \(p\)-Numbers
Summary: In this paper, we present a combinatorial interpretation of Leonardo \(p\)-numbers in terms of colored linear tilings and provide combinatorial proofs for several identities involving them. We further explore the incomplete and hyper Leonardo \(p\)-numbers, presenting their combinatorial interpretations.Belkhir, Amine, Tan, Elif
openaire +2 more sources
Gaussian Quaternion Involving Leonardo Numbers
Sarajevo Journal of MathematicsIn this study, using the Leonardo numbers, we define a new type of quaternion that is called a Leonard Gaussian quaternion. We also give a negative-Leonardo Gaussian quaternion. These numbers are introduced from the set of complex numbers and quaternions. Moreover, we obtain the Binet’s formula, generating function formula, d’Ocagne’s identity, Catalan’
openaire +2 more sources
2023
Abstract: In the paper, we define the $q$-Leonardo bicomplex numbers by using the $q$-integers. Also, we give some algebraic properties of $q$-Leonardo bicomplex numbers such as recurrence relation, generating function, Binet's formula, D'Ocagne's identity, Cassini's identity, Catalan's identity and Honsberger identity.
openaire +2 more sources
Abstract: In the paper, we define the $q$-Leonardo bicomplex numbers by using the $q$-integers. Also, we give some algebraic properties of $q$-Leonardo bicomplex numbers such as recurrence relation, generating function, Binet's formula, D'Ocagne's identity, Cassini's identity, Catalan's identity and Honsberger identity.
openaire +2 more sources
Some Properties of Leonardo Numbers
2020In this paper, we consider the Leonardo numbers which is defined by Catarino and Borges. Using Binet's formula of this sequence, we obtain new identities of the Leonardo numbers. Also , we give relations among the Fibonacci, Lucas and Leonardo numbers.
ALP, Yasemin, KOÇER, E. Gökçen
openaire +1 more source
Leonardo Numbers and their Bicomplex Extension
Nepal Journal of Mathematical SciencesThis 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.
Molhu Prasad Jaiswal +2 more
openaire +1 more source
Generalized Fibonacci–Leonardo numbers
Journal of Difference Equations and Applications, 2023Urszula Bednarz +1 more
openaire +1 more source