Results 21 to 30 of about 1,654,498 (260)
AIMS Mathematics, 2023 <abstract><p>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. Moreover, we presented a range of identities that provided deeper insights
Karataş, Adnan
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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 +2 more
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Hyper-Dual Leonardo Numbers [PDF]
, 2022 In the present paper, the hyper-dual Leonardo numbers will be introduced with the use of Leonardo numbers. Some algebraic properties of these numbers such as recurrence relation, generating function, Catalan’s and Cassini’s identity, Binet’s formula, sum formulas will also be obtained.
ÖZKALDI KARAKUŞ, Sıddıka +2 more
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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
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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 +1 more
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Logic Journal of the IGPLAbstract 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
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Some results on geometric circulant matrices involving the Leonardo numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn 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
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A Note on the Fuzzy Leonardo Numbers
Transactions on Fuzzy Sets and SystemsIn 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 +2 more
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, 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
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Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers
AxiomsThis 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 +3 more
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