Some Weighted Generalized Fibonacci Number Summation Identities, Part 2 [PDF]
arXiv, 2021 In part 1 of this paper some linear weighted generalized Fibonacci number summation identities were derived using the fact that the Fibonacci number is the residue of a rational function. In this part, using the same method, some quadratic and cubic weighted generalized Fibonacci number summation identities are derived, including some infinite series ...
M. J. Kronenburg
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On the Frobenius Number of Fibonacci Numerical Semigroups [PDF]
arXiv, 2006 In this paper we compute the Frobenius number of certain {\em Fibonacci numerical semigroups}, that is, numerical semigroups generated by a set of Fibonacci numbers, in terms of Fibonacci numbers.
J. M. MARIN +2 more
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Faber polynomial coefficient inequalities for bi-Bazilevič functions associated with the Fibonacci-number series and the square-root functions [PDF]
Journal of Inequalities and ApplicationsTwo new subclasses of the class of bi-Bazilevič functions, which are related to the Fibonacci-number series and the square-root functions, are introduced and studied in this article.
H. M. Srivastava +5 more
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Tunable multichannel Fibonacci one-dimensional terahertz photonic crystal filter [PDF]
Scientific Reports, 2023 This paper proposes a multichannel terahertz optical filter based on a one-dimensional photonic crystal with a third-order Fibonacci structure, including a bulk Dirac semimetal.
V. Sepahvandi, B. Rezaei, A. H. Aly
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Some properties of Fibonacci numbers, Fibonacci octonions, and generalized Fibonacci-Lucas octonions [PDF]
Advances in Difference Equations, 2015 In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.
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On the sum of a prime and a Fibonacci number [PDF]
International Journal of Number Theory, 2010 We show that the set of the numbers that are the sum of a prime and a Fibonacci number has positive lower asymptotic density.
K. S. Enoch Lee
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Number of Compositions and Convolved Fibonacci numbers [PDF]
arXiv, 2010 We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for Fibonacci numbers are proved.
Milan Janjić
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Generalized Fibonacci numbers and automorphisms of K3 surfaces with Picard number 2 [PDF]
arXivUsing the properties of generalized Fibonacci numbers, we determine the automorphism groups of some K3 surfaces with Picard number 2. Conversely, using the automorphisms of K3 surfaces with Picard number 2, we prove the criterion for a given integer n is to be a generalized Fibonacci number.
Kwangwoo Lee
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Statistics on restricted Fibonacci words [PDF]
Transactions on Combinatorics, 2021 We study two foremost Mahonian statistics, the major index and the inversion number for a class of binary words called restricted Fibonacci words. The language of restricted Fibonacci words satisfies recurrences which allow for the calculation of the ...
Omer Egecloglu
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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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