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Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]

Notes on Number Theory and Discrete Mathematics
We find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele, Olamide Esther Salami   +1 more
doaj   +1 more source

Matrices of Fibonacci Numbers

, 1981
The matrices of Fibonacci numbers (called windows) possess some unusual properties which are not shared by normal matrices, such as commutativity under multiplication and +1 for all determinants.
M.C. Er
core  

As formas e os números da natureza [PDF]

, 2004
TCC (graduação) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Curso de Matemática.Este trabalho trata de uma pesquisa intitulada: As formas e os números da natureza.O estudo mostrou que a seqüência de Fibonacci está ...
Wilberstaedt, Giorgio
core  

Mersenne k-Fibonacci numbers [PDF]

, 2016
For an integer k≥ 2, let (Fn(k))n be the k-Fibonacci sequence which starts with 0,...,0,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we find all k-Fibonacci numbers which are Mersenne numbers, i.e., k-Fibonacci
Carlos A. Gómez, Jhon J. Bravo, Gómez, Carlos A., Bravo, Jhon J.   +3 more
core   +1 more source

Generalized Fibonacci Numbers and Music [PDF]

, 2018
Mathematics and music have well documented historical connections. Just as the ordinary Fibonacci numbers have links with the golden ratio, this paper considers generalized Fibonacci numbers developed from generalizations of the golden ratio.
Robert van Gend, Anthony G Shannon, Shannon, Anthony G, Gend, Robert van, Klamka, Irina, Irina Klamka   +5 more
core   +1 more source

On Gaussian Leonardo numbers [PDF]

Contributions to Mathematics, 2023
Dursun Taşcı
doaj   +1 more source

On a problem of Pillai with Fibonacci numbers and powers of 3. [PDF]

Bol Soc Mat Mex, 2020
Ddamulira M.
europepmc   +1 more source

On The Generalized Gaussian Fibonacci Numbers.

Ars Comb., 2017
Many authors define certain generalizations of the usual Fibonacci, Pell and Lucas numbers by matrix methods and then obtain the Binet formulas and combinatorial representations of the generalizations of these number sequence. In this article firstly we define and study the generalized Gaussian Fibonacci numbers and then find the matrix representation ...
Lee, G.Y., Aşçı, Mustafa
openaire   +5 more sources

Aliquots sums of Fibonacci numbers [PDF]

, 2010
Here, we investigate the Fibonacci numbers whose sum of aliquot divisors is also a Fibonacci number (the prime Fibonacci numbers have this ...
Luca, Florian, Stănică, Pantelimon
core   +2 more sources

Some Properties of Generalized Apostol-Type Frobenius–Euler–Fibonacci Polynomials

Mathematics
In this paper, by using the Golden Calculus, we introduce the generalized Apostol-type Frobenius–Euler–Fibonacci polynomials and numbers; additionally, we obtain various fundamental identities and properties associated with these polynomials and numbers,
Maryam Salem Alatawi, Waseem Ahmad Khan, Can Kızılateş, Cheon Seoung Ryoo   +3 more
doaj   +1 more source