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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.
Bauer M +17 more
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Free Fibonacci Sequences [PDF]
, 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.
Avila, Brandon, Khovanova, Tanya
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Weak Disorder in Fibonacci Sequences [PDF]
Journal of Physics A: Mathematical and General, 2006 We study how weak disorder affects the growth of the Fibonacci series. We introduce a family of stochastic sequences that grow by the normal Fibonacci recursion with probability 1-epsilon, but follow a different recursion rule with a small probability ...
Ben-Naim E +8 more
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The quaternion-type cyclic-Fibonacci sequences in groups [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we define the six different quaternion-type cyclic-Fibonacci sequences and present some properties, such as, the Cassini formula and generating function. Then, we study quaternion-type cyclic-Fibonacci sequences modulo m.
Nazmiye Yilmaz +2 more
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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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Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences
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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On Third-Order Bronze Fibonacci Numbers
Mathematics, 2021 In this study, we firstly obtain De Moivre-type identities for the second-order Bronze Fibonacci sequences. Next, we construct and define the third-order Bronze Fibonacci, third-order Bronze Lucas and modified third-order Bronze Fibonacci sequences. Then,
Mücahit Akbiyik, Jeta Alo
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Some Algebraic Aspects of MorseCode Sequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 Morse code sequences are very useful to give combinatorial interpretations of various properties of Fibonacci numbers. In this note we study some algebraic and combinatorial aspects of Morse code sequences and obtain several q-analogues of Fibonacci
Johann Cigler
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Altered Numbers of Fibonacci Number Squared
Journal of New Theory, 2023 We investigate two types of altered Fibonacci numbers obtained by adding or subtracting a specific value $\{a\}$ from the square of the $n^{th}$ Fibonacci numbers $G^{(2)}_{F(n)}(a)$ and $H^{(2)}_{F(n)}(a)$.
Emre Kankal, Fikri Köken
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On the pulsating (m,c)-Fibonacci sequence
Heliyon, 2021 In this paper, we study new ideas in the generalization of additive and multiplicative pulsating Fibonacci sequences. Then, we construct two types of pulsating Fibonacci sequences of the mth order.
Kittipong Laipaporn +2 more
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