Results 21 to 30 of about 17,245 (264)

Binomial Coefficients and Lucas Sequences

Journal of Number Theory, 2002
Let sequences \(\{u_n\}_{n\geq 0}\) and \(\{v_n\}_{n\geq 0}\) be defined by \(u_n= \frac{a^n-b^n}{a-b}\), \(v_n= a^n+b^n\) where \(a,b\) are integers such that \(a>|b|\). (Such sequences are Lucas sequences such that the associated quadratic polynomial has integer roots.
Flammenkamp, Achim, Luca, Florian
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Generalized Bronze Leonardo sequence [PDF]

Notes on Number Theory and Discrete Mathematics
In this study, we define the Bronze Leonardo, Bronze Leonardo–Lucas, and Modified Bronze Leonardo sequences, and some terms of these sequences are given. Then, we give special summation formulas, special generating functions, etc.
Engin Özkan, Hakan Akkuş
doaj   +1 more source

Diophantine equations with Lucas and Fibonacci number coefficients [PDF]

Notes on Number Theory and Discrete Mathematics
Fibonacci and Lucas numbers are special number sequences that have been the subject of many studies throughout history due to the relations they provide.
Cemil Karaçam, Alper Vural, Bilal Aytepe, Ferhat Yıldız   +3 more
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Coincidences in Generalized Lucas Sequences

The Fibonacci Quarterly, 2014
For an integer $k\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized Lucas sequence which starts with $0,\ldots,0,2,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all the integers that appear in different generalized Lucas sequences; i.e., we study the Diophantine equation $L_n^{(k)}=L_m^{(\ell)
Bravo, Eric F., Bravo, Jhon J., Luca, Florian   +2 more
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On the k-Fibonacci and k-Lucas spinors [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this paper, we introduce a new family of sequences called the k-Fibonacci and k-Lucas spinors. Starting with the Binet formulas we present their basic properties, such as Cassini’s identity, Catalan’s identity, d’Ocagne's identity, Vajda's identity ...
Munesh Kumari, Kalika Prasad, Robert Frontczak   +2 more
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Repdigits in k-Lucas sequences

Proceedings - Mathematical Sciences, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bravo, Jhon J., Luca, Florian
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The nth Power of Generalized (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties

Journal of New Theory, 2021
In this study, new formulas for the nth power of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas special matrix sequences are established by using determinant and trace of the matrices.
Şükran Uygun
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On the Incomplete Edouard and Incomplete Edouard–Lucas Numbers

Mathematics
This study introduces two new sequences: the incomplete Edouard and the incomplete Edouard–Lucas numbers. In addition, we establish some of the properties, identities, and recurrence relations of these sequences. The relations of these new sequences with
Elen Viviani Pereira Spreafico, Eudes Antonio Costa, Paula Catarino   +2 more
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On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers

Axioms, 2023
Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number systems.
Elen Viviani Pereira Spreafico, Paula Catarino, Paulo Vasco   +2 more
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On New Polynomial Sequences Constructed to Each Vertex in an n-Gon

Discrete Dynamics in Nature and Society, 2022
In this work, we bring to light the properties of newly formed polynomial sequences at each vertex of Pell polynomial sequences placed clockwise at each vertex in the n-gon. We compute the relation among the polynomials with such vertices.
Abdul Hamid Ganie, Engin ŏzkan, Mine Uysal, Afroza Akhter   +3 more
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