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Diophantine equations with Lucas and Fibonacci number coefficients [PDF]
Notes on Number Theory and Discrete MathematicsFibonacci 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 +3 more
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Generalized Fibonacci sequences in groupoids [PDF]
Advances in Difference Equations, 2013 Abstract In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents. Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized Fibonacci ...
Kim, Hee, Neggers, J, So, Keum
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Exploring Generalized $2^k$-Fibonacci Sequence: A New Family of the Fibonacci Sequence
Communications in Advanced Mathematical SciencesThe focus of this paper is to study the $2^k$–Fibonacci sequence, which is defined for all integers $2^k$, and its connections with both the Fibonacci and the Fibonacci-Lucas sequences.
Elis Gardel Costa Mesquista +2 more
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Weak disorder in Fibonacci sequences [PDF]
Journal of Physics A: Mathematical and General, 2006 4 pages, 2 ...
Ben-Naim, E., Krapivsky, P. L.
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Copper ratio obtained by generalizing the Fibonacci sequence
AIP AdvancesIn this study, we define a new generalization of the Fibonacci sequence that gives the copper ratio, and we will call it the copper Fibonacci sequence. In addition, inspired by the copper Fibonacci definition, we also define copper Lucas sequences, and ...
Engin Özkan, Hakan Akkuş
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Transformations of Pythagorean triples generated by generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsWe present matrices that transform Pythagorean triples arising from generalized Fibonacci sequences into other such triples. We also show that entries in the powers of such matrices can be expressed in terms of generalized Fibonacci sequences.
Jathan Austin
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Elliptic Solutions of Dynamical Lucas Sequences
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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Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences [PDF]
Turkish Journal of Analysis and Number Theory, 2016 The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula Fn=Fn-1+Fn-2, , and F0=0, F1=1, where Fn is a nth number of sequence.
Yogesh Kumar Gupta +2 more
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A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence [PDF]
Sahand Communications in Mathematical Analysis, 2019 In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis.
Moosa Ebadi, Farnaz Soltanpour
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Trees and Meta-Fibonacci Sequences [PDF]
The Electronic Journal of Combinatorics, 2009 For $k>1$ and nonnegative integer parameters $a_p, b_p$, $p = 1..k$, we analyze the solutions to the meta-Fibonacci recursion $C(n)=\sum_{p=1}^k C(n-a_p-C(n-b_p))$, where the parameters $a_p, b_p$, $p = 1..k$ satisfy a specific constraint. For $k=2$ we present compelling empirical evidence that solutions exist only for two particular families of ...
Isgur, Abraham +2 more
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