Results 31 to 40 of about 2,715 (213)
, 2014 This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: given n, sum the previous two terms and divide them by the largest possible power of n. The behavior of such sequences depends on n. We analyze these sequences for small n: 2, 3, 4, and 5. Surprisingly these behaviors are very different.
Avila, Brandon, Khovanova, Tanya
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New Fibonacci-type pulsated sequences [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 A new Fibonacci-type sequence from pulsated type is introduced. The explicit form of its members is given.
Lilija Atanassova, Velin Andonov
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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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Accelerations of Generalized Fibonacci Sequences [PDF]
The Fibonacci Quarterly, 2011 In this paper we study how to accelerate the convergence of the ratios (x_n) of generalized Fibonacci sequences. In particular, we provide recurrent formulas in order to generate subsequences (x_{g_n}) for every linear recurrent sequence (g_n) of order 2.
Marco Abrate +3 more
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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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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, cross product and mixed product for the hyperbolic Fibonacci vectors.
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On Recursive Hyperbolic Fibonacci Quaternions
Communications in Advanced Mathematical Sciences, 2021 Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers.
Ahmet Daşdemir
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LINEARLIZATION OF GENERALIZED FIBONACCI SEQUENCES [PDF]
Korean Journal of Mathematics, 2014 Summary: In this paper, we give linearization of generalized Fibonacci sequences \(\{g_n\}\) and \(\{q_n\}\), respectively, defined by Gupta et al. and Edson et al. and use this result to give the matrix form of the \(n\)-th power of a companion matrix of \(\{g_n\}\) and \(\{q_n\}\). Then we re-prove the Cassini's identity for \(\{g_n\}\) and \(\{q_n\}\
Jang, Young Ho, Jun, Sang Pyo
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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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