Results 211 to 220 of about 12,049 (240)
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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 in- troduce the bicomplex Leonardo numbers. Also, we give some algebraic prop- erties of bicomplex Leonardo numbers such as recurrence relation, generating function, Binet's formula, D'Ocagne's identity ...
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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 in- troduce the bicomplex Leonardo numbers. Also, we give some algebraic prop- erties of bicomplex Leonardo numbers such as recurrence relation, generating function, Binet's formula, D'Ocagne's identity ...
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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
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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
Taher, Hunar Sherzad, Dash, Saroj Kumar
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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’
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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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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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Generalized Fibonacci–Leonardo numbers
Journal of Difference Equations and Applications, 2023Urszula Bednarz +1 more
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Leonardo da Vinci and Fluid Mechanics
Annual Review of Fluid Mechanics, 2021Susan Broomhall, Ivan Marusic
exaly