Results 31 to 40 of about 919 (183)
Note on a Fibonacci parity sequence
Cryptography and Communications, 2022 Let ftm = 0111010010001... be the analogue of the Thue-Morse sequence in Fibonacci representation. In this note we show how, using the Walnut theorem-prover, to obtain a measure of its complexity, previously studied by Jamet, Popoli, and Stoll. We strengthen one of their theorems and disprove one of their conjectures.
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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 ...
Abraham Isgur +2 more
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Generalized Fibonacci-like sequence and Fibonacci sequence
International Journal of Contemporary Mathematical Sciences, 2014 Every term in the Fibonacci Sequence can be determined recursively with the help of initial values F0 = 0, F1 = 1. Similar is the case with Lucas Sequence. In this paper, we study Generalized Fibonacci-Like sequence {Dn} defined by the recurrence relation Dn = Dn-1 + Dn-2, for all n 2 with D0 = 2 and D1 = 1+m, m being a fixed positive integer.
Sanjay Harne +2 more
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Generalized Fibonacci Sequences for Elliptic Curve Cryptography
Mathematics, 2023 The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves.
Zakariae Cheddour +2 more
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On Period of the Sequence of Fibonacci Polynomials Modulo
Discrete Dynamics in Nature and Society, 2013 It is shown that the sequence obtained by reducing modulo coefficient and exponent of each Fibonacci polynomials term is periodic. Also if is prime, then sequences of Fibonacci polynomial are compared with Wall numbers of Fibonacci sequences according ...
İnci Gültekin, Yasemin Taşyurdu
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Generalization of the 2-Fibonacci sequences and their Binet formula [PDF]
Notes on Number Theory and Discrete MathematicsWe will explore the generalization of the four different 2-Fibonacci sequences defined by Atanassov. In particular, we will define recurrence relations to generate each part of a 2-Fibonacci sequence, discuss the generating function and Binet formula of ...
Timmy Ma, Richard Vernon, Gurdial Arora
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Fibonacci Modules and Multiple Fibonacci Sequences
Ars Comb., 2008 Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.
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On the Periods of 2-Step General Fibonacci Sequences in the Generalized Quaternion Groups
Discrete Dynamics in Nature and Society, 2012 We study 2-step general Fibonacci sequences in the generalized quaternion groups Q4n. In cases where the sequences are proved to be simply periodic, we obtain the periods of 2-step general Fibonacci sequences.
Bahram Ahmadi, Hossein Doostie
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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 Natural Density DF(Fk) of Fibonacci Word
Vestnik KRAUNC: Fiziko-Matematičeskie NaukiThis paper explores profound generalizations of the Fibonacci sequence, delving into random Fibonacci sequences, k-Fibonacci words, and their combinatorial properties.
Abdullah, D., Hamoud, J.
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