Results 81 to 90 of about 394,323 (159)

On a Matrix Formulation of the Sequence of Bi-Periodic Fibonacci Numbers

Axioms
In this study, we investigate some new properties of the sequence of bi-periodic Fibonacci numbers with arbitrary initial conditions, through an approach that combines the matrix aspect and the fundamental Fibonacci system.
Mustapha Rachidi, Elen V. P. Spreafico, Paula Catarino   +2 more
doaj   +1 more source

On the sum of reciprocal generalized Fibonacci numbers [PDF]

arXiv, 2015
In this paper, 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.
arxiv  

Edge-Disjoint Fibonacci Trees in Hypercube

Journal of Computer Networks and Communications, 2014
The Fibonacci tree is a rooted binary tree whose number of vertices admit a recursive definition similar to the Fibonacci numbers. In this paper, we prove that a hypercube of dimension h admits two edge-disjoint Fibonacci trees of height h, two edge ...
Indhumathi Raman, Lakshmanan Kuppusamy
doaj   +1 more source

Four New Generalized Fibonacci Number Summation Identities [PDF]

arXiv, 2018
Two new generalized Fibonacci number summation identities are stated and proved, and two other new generalized Fibonacci number summation identities are derived from these, of which two special cases are already known in literature.
arxiv  

On Certain Properties of Parametric Kinds of Apostol-Type Frobenius–Euler–Fibonacci Polynomials

Axioms
This paper presents an overview of cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials, as well as several identities that are associated with these polynomials.
Hao Guan, Waseem Ahmad Khan, Can Kızılateş, Cheon Seoung Ryoo   +3 more
doaj   +1 more source

Identities and Generating Functions of Products of Generalized Fibonacci numbers, Catalan and Harmonic Numbers [PDF]

arXiv
We considered the properties of generalized Fibonacci and Lucas numbers class. The analogues of well-known Fibonacci identities for generalized numbers are obtained. We gained a new identity of product convolution of generalized Fibonacci and Lucas numbers.
arxiv  

Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers [PDF]

arXiv, 2007
The three anti-commutative two-dimensional Pauli Pascal triangles can be generalized into multi-dimensional Pauli Pascal hyperpyramids. Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci numbers, Pauli Jacobsthal numbers, and Pauli Fibonacci numbers of higher order. And the question is: are Pauli rabbits killer rabbits?
arxiv  

Three closed forms for convolved Fibonacci numbers

Results in Nonlinear Analysis, 2020
In the paper, by virtue of the Faà di Bruno formula and several properties of the Bell polynomials of the second kind, the author computes higher order derivatives of the generating function of convolved Fibonacci numbers and, consequently, derives three
Feng Qi
doaj  

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

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

Generalized Fibonacci numbers and automorphisms of K3 surfaces with Picard number 2 [PDF]

arXiv
Using 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.
arxiv