Results 81 to 90 of about 919 (183)
Another six Fibonacci-like sequences [PDF]
Notes on Number Theory and Discrete MathematicsWe briefly describe six Fibonacci-like sequences or arbitrary order that give rise to a periodic or eventually periodic sequences. We provide some examples and demonstrate the explicit periods of these sequences.
Karol Gryszka
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On a generalization of the Hosoya triangle [PDF]
Notes on Number Theory and Discrete MathematicsThis paper introduces the Fibonacci polynomial triangle, inspired by the structure of the Hosoya triangle and constructed using Fibonacci polynomials.
Turhan Çifçi +2 more
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A class of Fibonacci-type sequences
Discrete Mathematics, 1974 Let \(\{L_n : n\ge 1\}\) be a sequence of the form \[ L_n= \min\left( \sum_{j=1}^p L_{n-a_j}\quad (n>e),\quad \sum_{j=1}^q L_{n-b_j}\quad (n>e)\right), \] where \(\{a_j\}\) and \(\{b_j\}\) are positive integers, and \(e = \max_{i,j} \{a_i ,b_j\}\). A necessary and sufficient condition on the integers \(\{a_j\}\) and \(\{b_j\}\) is given so that, for ...
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Psychoacoustic Properties of Fibonacci Sequences
Acta Polytechnica, 2008 1202, Fibonacci set up one of the most interesting sequences in number theory. This sequence can be represented by so-called Fibonacci Numbers, and by a binary sequence of zeros and ones.
J. Sokoll, S. Fingerhuth
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A Family of Fibonacci-Like Sequences
The Fibonacci Quarterly, 1987 We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_0 = G_1 = 1$, and we express $G_n$ in terms of the Fibonacci numbers $F_n$ and $F_{n-1}$, and in the parameters $\alpha_1,\ldots,\alpha_k$.
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More generalized k(ε)-Fibonacci sequence, series, and its applications
AIP AdvancesIn this study, we present a generalized higher-order delta operator with the co-efficient of falling factorial and its inverse, both of which allow us to get more generalized k(ε)-Fibonacci sequences along with their sums, a few theorems, and some ...
Rajiniganth P +3 more
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Some Fibonacci-Related Sequences
The Fibonacci QuarterlyWe discuss an interesting sequence defined recursively; namely, sequence A105774 from the On-Line Encyclopedia of Integer Sequences, and study some of its properties. Our main tools are Fibonacci representation, finite automata, and the Walnut theorem-prover. We also prove two new results about synchronized sequences.
Benoit Cloitre, Jeffrey Shallit
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Random Fibonacci Words via Clone Schur Functions
Forum of Mathematics, SigmaWe investigate positivity and probabilistic properties arising from the Young–Fibonacci lattice $\mathbb {YF}$ , a 1-differential poset on words composed of 1’s and 2’s (Fibonacci words) and graded by the sum of the digits.
Leonid Petrov, Jeanne Scott
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Generalized Fibonacci Sequences Generated from a $k$--Fibonacci Sequence
Journal of Mathematics Research, 2012 In this paper we will prove that all $k$--Fibonacci sequence contains generalized Fibonacci sequences and we will indicate the form of obtain them.
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Visualization of Metallic Sequences and its Extensions: A Combinatorial approach Via Board and Tiles
REDIMATThe study of recurring numerical sequences interests numerous researchers in several countries. We observe that, with a historical legacy from the Fibonacci and Lucas sequences, numerous ways of approaching and generalizing these and other sequences ...
Francisco Regis Vieira Alves +2 more
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