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The Log-Behavior of Some Sequences Related to the Generalized Leonardo Numbers
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Chaos, Solitons & Fractals, 2021
Abstract Until today, many researchers have studied related to hybrid numbers which are a generalization of complex, hyperbolic and dual numbers. In this paper, using the Leonardo numbers, we introduce the hybrid Leonardo numbers. Also, we give some algebraic properties of the hybrid Leonardo numbers such as recurrence relation, generating function ...
Yasemin Alp, E. Gokcen Kocer
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Abstract Until today, many researchers have studied related to hybrid numbers which are a generalization of complex, hyperbolic and dual numbers. In this paper, using the Leonardo numbers, we introduce the hybrid Leonardo numbers. Also, we give some algebraic properties of the hybrid Leonardo numbers such as recurrence relation, generating function ...
Yasemin Alp, E. Gokcen Kocer
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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 ...
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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 ...
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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.
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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.
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Fibonacci Numbers that Are $$\eta$$-concatenations of Leonardo and Lucas Numbers
Proceedings of the Bulgarian Academy of SciencesLet $$\{F_{r}\}_{r\geq0}$$, $$\{L_{r}\}_{r\geq0}$$ and $$\{Le_{r}\}_{r\geq0}$$ be $$r$$-th terms of Fibonacci, Lucas and Leonardo sequences, respectively. In this paper, we determined the effective bounds for the solutions of the Diophantine equation $$F_{r}=\eta^{k}Le_{s}+L_{t}$$ in non-negative integers $$r$$, $$s$$, $$t$$, where $$k$$ represents the
Hunar Taher, Saroj Dash
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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
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Generalized Fibonacci–Leonardo numbers
Journal of Difference Equations and Applications, 2023Urszula Bednarz +1 more
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Recent progress in the treatment of cancer in children
Ca-A Cancer Journal for Clinicians, 2021Theodore W Laetsch
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