Results 11 to 20 of about 903 (200)
A Context-Free Grammar Associated with Fibonacci and Lucas Sequences
Journal of Mathematics, 2023 We introduce a context-free grammar G=s⟶s+d,d⟶s to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula.
Harold Ruilong Yang
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Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences [PDF]
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu +1 more
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Equations with Solution in Terms of Fibonacci and Lucas Sequences [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 The main results characterize the equations (2.1) and (2.10) whose solutions are linear combinations with rational coefficients of at most two terms of classical Fibonacci and Lucas sequences.
Andreescu Titu, Andrica Dorin
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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
Michael J. Schlosser, Meesue Yoo
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Fibonacci and k Lucas Sequences as Series of Fractions [PDF]
Mathematical Journal of Interdisciplinary Sciences, 2016 In this paper, we defined new relationship between k Fibonacci and k Lucas sequences using continued fractions and series of fractions, this approach is different and never tried in k Fibonacci sequence literature.
A. D. Godase, M. B. Dhakne
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Some identities for generalized Fibonacci and Lucas sequences [PDF]
, 2013 In this study, we define a generalization of Lucas sequence {pn}. Then we obtain Binet formula of sequence {pn}. Also, we investigate relationships between generalized Fibonacci and Lucas sequences. © 2013, Hacettepe University. All rights reserved.
IRMAK, Nurettin, ALP, Murat
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On some new results for the generalised Lucas sequences
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica Dorin +2 more
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On Fibonacci and Lucas sequences modulo a prime and primality testing
Arab Journal of Mathematical Sciences, 2018 We prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p∣Fp−p5. We then discuss these results in the context of primality testing.
Dorin Andrica +2 more
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Relations between Generalized Bi-Periodic Fibonacci and Lucas Sequences
Mathematics, 2020 In this paper we consider a generalized bi-periodic Fibonacci {fn} and a generalized bi-periodic Lucas sequence {qn} which are respectively defined by f0=0, f1=1, fn=afn−1+cfn−2 (n is even) or fn=bfn−1+cfn−2 (n is odd), and q0=2d, q1=ad, qn=bqn−1+cqn−2 ...
Younseok Choo
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Generalizations of Fibonacci and Lucas sequences [PDF]
, 2002 The author studies the Hecke group \(H(\sqrt q)\) (\(q\) a prime \(\geq 5\)), the subgroup of \(\text{PSL}(2, \mathbb{Z})\) generated by \(z \to {- {1/z}}\) and \(z \to {z + \sqrt q}\). This group can also be generated by \(z \to {- {1/z}}\) and an element \(S\) whose matrix representation is \[ \left(\begin{matrix} 0 & {-1} \\ 1 & {\sqrt q} \end ...
Yilmaz Özgür, Nihal
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