Results 21 to 30 of about 94,026 (132)
, 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.
Sıddıka Özkaldı Karakuş +2 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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Leonardo and hyper-Leonardo numbers via Riordan arrays
Ukrains’kyi Matematychnyi ZhurnalUDC 511 A generalization of the Leonardo numbers is defined and called the hyper-Leonardo numbers. Infinite lower triangular matrices, whose elements are Leonardo and hyper-Leonardo numbers are considered. Then the A - and Z -sequences of these matrices are obtained. Finally, the combinatorial identities between the hyper-Leonardo and Fibonacci
Yasemin Alp, E. Gökçen Koçer
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A New Family of Number Sequences: Leonardo-Alwyn Numbers
Armenian Journal of Mathematics, 2023 In this study, we define a new type of number sequence called Leonardo-Alwyn sequence. We obtain the Binet formula, generating function and some relations for these numbers. Moreover, we give the matrix representation of the Leonardo-Alwyn numbers.
Hasan Gökbaş
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, 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.
Fügen Torunbalcı Aydın
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On the norms and Hadamard product of Toeplitz matrices involving Leonardo numbers [PDF]
Mathematica MoravicaIn this study, we consider the Toeplitz matrices with entries being Leonardo numbers. We have found upper and lower bounds for the spectral norms of these matrices, considering also the Hadamard product of this type of matrix.
Catarino Paula +4 more
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Some Properties of Leonardo Numbers
, 2021 In 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.
Yasemin Alp, E. Gökçen Koçer
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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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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’
Hasan Gökbaş
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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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