Results 111 to 120 of about 976 (217)
Closed formulas for finite sums of weighted fractional generalized fibonacci products [PDF]
, 2018 © 2018 Fibonacci Association. All rights reserved. In this paper, we present closed formulas for finite sums of fractions involving weighted products of generalized Fibonacci numbers. There are two significant features that characterize the main results.
Melham, RS
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Generalized Fibonacci Dynamical Systems [PDF]
, 2009 In this paper we consider generalizations of dynamical systems that are based on the Fibonacci sequence. We first study stability properties of such systems for both the continuous and discrete–time case.
Balestrino, A +2 more
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A Comprehensive Survey of Dual Generalized Complex Fibonacci Numbers [PDF]
, 2020 The aim of this paper is to develop dual-generalized complex Fibonacci numbers, special type of Horadam sequence. Moreover, the general recurrence relations of dual-generalized complex Fibonacci and Lucas numbers are obtained.
Şentürk, Gülsüm Yeliz +2 more
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On Some Inequalities with Fibonacci Numbers via Weighted Reverse Hölder Inequalities
Annales Mathematicae SilesianaeIn this paper, we introduce new inequalities for weighted sums of powers. By utilizing known Fibonacci identities alongside our generalized inequalities, we derive new sequences of inequalities for Fibonacci numbers.
Pribanić Anamarija Perušić
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On the Generalized Order-$k$ Fibonacci and Lucas Numbers
Rocky Mountain Journal of Mathematics, 2006 In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.
Kiliç, Emrah, Taşci, Dursun
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A Combinatorial Interpretation of the Generalized Fibonacci Numbers
Advances in Applied Mathematics, 1997 The author considers the Fibonacci numbers of order \(k\), i.e., the numbers \(F^{(k)}_n\) defined by the recurrence relation \(F^{(k)}_{n+ k}= F_{n+k-1}^{(k)}+ F_{n+ k-2}^{(k)}+\cdots+ F_{n+1}^{(k)}+ F^{(k)}_n\) and, as in \textit{D. E. Knuth} [The art of computer programming, Vol. 3, Addison-Wesley (1974; Zbl 0302.68010)], by the initial conditions \(
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Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers
, 2005 In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.
Egge, Eric C., Mansour, Toufik
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A determinant of generalized Fibonacci numbers
Journal of Combinatorics and Number Theory, 2012 We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of them extending Cassini's identity for Fibonacci numbers.
Krattenthaler, Christian +1 more
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Generalization of the Distance Fibonacci Sequences
AxiomsIn this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties ...
Nur Şeyma Yilmaz +2 more
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Weighted sum of the sixth powers of Horadam numbers [PDF]
Notes on Number Theory and Discrete MathematicsOhtsuka and Nakamura found simple formulas for Σⁿⱼ₌₁Fⱼ⁶ and Σⁿⱼ₌₁Lⱼ⁶, where Fₖ and Lₖ are the k-th Fibonacci and Lucas numbers, respectively. In this note we extend their results to a general second order sequence by deriving a formula for Σⁿⱼ₌₁(-1/q³ ...
Kunle Adegoke +2 more
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