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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
openaire   +2 more sources

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
doaj   +1 more source

On the complex factorization of the Lucas sequence

Applied Mathematics Letters, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bozkurt, S. Burcu, Yilmaz, Fatih, Bozkurt, Durmus   +2 more
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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
doaj  

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
doaj   +1 more source

pohl-michel/Lucas-Kanade-pyramidal-optical-flow-for-3D-image-sequences: 3rd release

, 2021
<p>Implementation of the Lucas-Kanade pyramidal optical flow algorithm to register 3D medical images A factor involved in the spatial gradients calculation, that was wrong in the previous version, has been corrected.</p ...
Pohl Michel
core   +1 more source

A generalization of Lucas polynomial sequence

Discrete Applied Mathematics, 2009
The authors consider the problem of a generalization of Lucas polynomial sequence. They obtain a generalized Lucas polynomial sequence from the lattice paths for the Delannoy numbers by allowing weights on the steps \((1,0),(0,1)\) and \((1,1)\).
Gi-Sang Cheon, Hana Kim, Louis W. Shapiro   +2 more
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On Power Sums Involving Lucas Functions Sequences [PDF]

, 2017
We present some general formulas related to sum of powers, also with alternating sign, involving Lucas functions sequences. In particular, our formulas give a synthesis of various identities involving sum of powers of well-known polynomial sequences such
Stefano Barbero
core   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source