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Coincidences in generalized Lucas sequences [PDF]
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.
Bravo, Eric F. +2 more
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The GCD Sequences of the Altered Lucas Sequences [PDF]
Annales Mathematicae Silesianae, 2020 In this study, we give two sequences {L+n}n≥1 and {L−n}n≥1 derived by altering the Lucas numbers with {±1, ±3}, terms of which are called as altered Lucas numbers.
Koken Fikri
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Blocks within the period of Lucas sequence
Ratio Mathematica, 2021 In this paper, we consider the periodic nature of the sequence of Lucas numbers L_n defined by the recurrence relation L_n= L_(n-1)+L_(n-2); for all n≥2; with initial condition L_0=2 and L_1=1.
Rima P. Patel, Dr. Devbhadra V. Shah
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Elliptic Solutions of Dynamical Lucas Sequences [PDF]
Entropy, 2021 We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences
Schlosser, Michael J., Yoo, Meesue
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Encryption and Decryption of the Data by Using the Terms of the Lucas Series
Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2021 The sequence, whose initial condition is 2 and 1, obtained by summing the two terms preceding it, is called the Lucas sequence. The terms of this series continue as 2, 1, 3, 4, 7, 11, 18, 29, ... respectively. The features of the Lucas sequence have been
Mehmet Duman, Merve Güney Duman
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Mathematica Bohemica, 2021 Summary: Let \((G_{n})_{n\geq 1}\) be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are \(\{U_n\}\) and \(\{V_n\}\), respectively. We show that the Diophantine equation \(G_n=B\cdot(g^{lm}-1)/(g^{l}-1)\) has only finitely many solutions in \(n,m\in\mathbb{Z}^+\), where \(g\geq 2 ...
Hayder Raheem Hashim, Szabolcs Tengely
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On Generalized Jacobsthal and Jacobsthal–Lucas Numbers
Annales Mathematicae Silesianae, 2022 Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
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Symmetric and generating functions of generalized (p,q)-numbers
Kuwait Journal of Science, 2021 In this paper, we first define new generalization for (p,q)-numbers. Considering these sequence, we give Binet's formulas and generating functions of (p,q)-Fibonacci numbers, (p,q)-Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q ...
Nabiha Saba +2 more
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Oscillatory Nonautonomous Lucas Sequences [PDF]
International Journal of Differential Equations, 2009 The oscillatory behavior of the solutions of the second‐order linear nonautonomous equation x(n + 1) = a(n)x(n) − b(n)x(n − 1), n ∈ ℕ0, where a, b : ℕ0 → ℝ, is studied. Under the assumption that the sequence b(n) dominates somehow a(n), the amplitude of the oscillations and the asymptotic behavior of its solutions are also analized.
Ferreira, José M., Pinelas, Sandra
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A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
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