Results 81 to 90 of about 1,163,753 (215)

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  

Generalizations of Fibonacci-Lucas inverse tangent summation identities of Hoggatt and Ruggels [PDF]

arXiv, 2019
We derive generalizations of a couple of inverse tangent summation identities involving Fibonacci and Lucas numbers. As byproducts we establish many new inverse tangent identities involving the Fibonacci and Lucas numbers.
arxiv  

Some Finite Sums Involving Generalized Fibonacci and Lucas Numbers

Discrete Dynamics in Nature and Society, 2011
By considering Melham's sums (Melham, 2004), we compute various more general nonalternating sums, alternating sums, and sums that alternate according to (−1)2𝑛+1 involving the generalized Fibonacci and Lucas numbers.
E. Kılıç, N. Ömür, Y. T. Ulutaş
doaj   +1 more source

Determinantal and Permanental Representation of Generalized Fibonacci Polynomials [PDF]

arXiv, 2011
In this paper, we give some determinantal and permanental representations of Generalized Fibonacci Polynomials by using various Hessenberg matrices. These results are general form of determinantal and permanental representations of k sequences of the generalized order-k Fibonacci and Pell numbers.
arxiv  

Determinants Containing Powers of Generalized Fibonacci Numbers [PDF]

arXiv, 2015
We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These studies have led us to discover a fundamental identity of determinant involving powers of linear polynomials. Finally,
arxiv  

Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers [PDF]

, 2005
Eric C. Egge, Toufik Mansour
openalex   +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  

Labeled Fibonacci Trees [PDF]

Legendre S. 2015. Labeled Fibonacci trees. The Fibonacci Quarterly 53: 152-167, 2014
The study describes a class of integer labelings of the Fibonacci tree, the tree of descent introduced by Fibonacci. In these labelings, Fibonacci sequences appear along ascending branches of the tree, and it is shown that the labels at any level are consecutive integers. The set of labeled trees is a commutative group isomorphic to $\mathbb{Z}^2$, and
arxiv  

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  

Some Theorems Involving Powers of Generalized Fibonacci Numbers at Non-Equidistant Points [PDF]

, 2007
Paul S. Bruckman, R. S. Melham
openalex   +1 more source