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Universal Journal of Mathematics and Applications, 2019 In this paper, we investigate the hyperbolic Fibonacci sequence and the hyperbolic Fibonacci numbers. Furthermore, we give recurrence relations, the golden ratio and Binet's formula for the hyperbolic Fibonacci sequence and Lorentzian inner product ...
Fügen Torunbalcı Aydın
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Weakly unconditionally Cauchy series and Fibonacci sequence spaces. [PDF]
J Inequal Appl, 2017 We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of ...
Kama R, Altay B.
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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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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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On the 2k-step Jordan-Fibonacci sequence
Advances in Difference Equations, 2017 In this paper, we define the 2k-step Jordan-Fibonacci sequence, and then we study the 2k-step Jordan-Fibonacci sequence modulo m. Also, we obtain the cyclic groups from the multiplicative orders of the generating matrix of the 2k-step Jordan-Fibonacci ...
Omur Deveci, Sait Taş, A Kılıçman
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p -Regularity of the p -Adic Valuation of the Fibonacci Sequence [PDF]
The Fibonacci quarterly, 2015 We show that the p-adic valuation of the sequence of Fibonacci numbers is a p-regular sequence for every prime p. For p 6= 2, 5, we determine that the rank of this sequence is α(p) + 1, where α(m) is the restricted period length of the Fibonacci sequence
Luis A. Medina, E. Rowland
semanticscholar +4 more sources
Researches on Mathematical Relationship of Five Elements of Containing Notes and Fibonacci Sequence Modulo 5 [PDF]
The Scientific World Journal, 2015 Considering the five periods and six qi’s theory in TCM almost shares a common basis of stem-branch system with the five elements of containing notes, studying the principle or mathematical structure behind the five elements of containing notes can ...
Zhaoxue Chen
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The complex-type cyclic-Fibonacci sequence and its applications [PDF]
Journal of Mahani Mathematical Research, 2023 In the present paper, we aim to generalize the notion of complex-type Fibonacci sequences to complex-type cyclic Fibonacci sequences. Firstly, we define the complex-type cyclic-Fibonacci sequence and then we give miscellaneous properties of this ...
Ömür Deveci +2 more
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Notes on generalized and extended Leonardo numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 This paper both extends and generalizes recently published properties which have been developed by many authors for elements of the Leonardo sequence in the context of second-order recursive sequences.
Anthony G. Shannon +2 more
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Random Fibonacci sequences [PDF]
Journal of Physics A: Mathematical and General, 2001 Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1} decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently small (large) B. In the limits B --> 0 and B --> infinity, we expand the Lyapunov exponent lambda(B) in powers of B and B^{-1}, respectively.
Sire, Clément, Krapivsky, Paul L.
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