Results 1 to 10 of about 1,804,204 (295)
Some properties of Fibonacci numbers, Fibonacci octonions and generalized Fibonacci-Lucas octonions [PDF]
arXiv, 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 ...
Savin, Diana
core +5 more sources
Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers [PDF]
Mathematics, 2018 The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our
Yuankui Ma, Wenpeng Zhang
doaj +3 more sources
Mathematics, 2021 In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously.
Natalia Bednarz
doaj +2 more sources
On a problem of Pillai with Fibonacci numbers and powers of 3. [PDF]
Bol Soc Mat Mex, 2020 Consider the sequence $$ \{{F}_{n}\}_{n \ge 0} $$ { F n } n ≥ 0 of Fibonacci numbers defined by $${F}_0=0$$ F 0 = 0 , $${F}_1 =1$$ F 1 = 1 , and $${F}_{{n}+2}= {F}_{{n}+1}+ {F}_{n} $$ F n + 2 = F n + 1 + F n for all $$ n\ge 0 $$ n ≥ 0 . In this paper, we
Ddamulira M.
europepmc +3 more sources
On the Harmonic and Hyperharmonic Fibonacci Numbers [PDF]
Advances in Difference Equations, 2015 In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which is finite sums
Kesim, Seyhun +2 more
core +6 more sources
On the Sum of Reciprocal Generalized Fibonacci Numbers [PDF]
Abstract and Applied Analysis, 2014 We consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.
Pingzhi Yuan, Zilong He, Junyi Zhou
doaj +4 more sources
Fibonacci numbers and orthogonal polynomials [PDF]
Arab Journal of Mathematical Sciences, 2008 We prove that the sequence $(1/F_{n+2})_{n\ge 0}$ of reciprocals of the Fibonacci numbers is a moment sequence of a certain discrete probability, and we identify the orthogonal polynomials as little $q$-Jacobi polynomials with $q=(1-\sqrt{5})/(1+\sqrt{5})
Berg, Christian
core +8 more sources
Generalized Fibonacci Numbers and Blackwell's Renewal Theorem [PDF]
, 2010 We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers.
Asmussen +9 more
core +2 more sources
On the Norms of Circulant and $r-$Circulant Matrices With the Hyperharmonic Fibonacci Numbers [PDF]
Journal of Inequalities and Applications, (2015) 2015:253, 2015 In this paper, we study norms of circulant and $r-$circulant matrices involving harmonic Fibonacci and hyperharmonic Fibonacci numbers.
Kizilateş, Can, Tuglu, Naim
core +2 more sources
On the arrowhead-Fibonacci numbers
Open Mathematics, 2016 In this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the k-step Fibonacci sequence and then we give some of their properties.
Gültekin Inci, Deveci Ömür
doaj +4 more sources