Results 81 to 90 of about 16,304 (189)

Generalized Finite-Length Fibonacci Sequences in Healthy and Pathological Human Walking: Comprehensively Assessing Recursivity, Asymmetry, Consistency, Self-Similarity, and Variability of Gaits. [PDF]

Front Hum Neurosci, 2021
Verrelli CM, Iosa M, Roselli P, Pisani A, Giannini F, Saggio G.   +5 more
europepmc   +1 more source

A New Notion of Convergence Defined by The Fibonacci Sequence: A Novel Framework and Its Tauberian Conditions

Mathematics
The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships.
Ibrahim S. Ibrahim, María C. Listán-García   +1 more
doaj   +1 more source

New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we introduce a set of identities involving hyperbolic k-Fibonacci quaternions and k-Lucas quaternions. Moreover, we derive summation identities for hyperbolic k-Fibonacci and k-Lucas quaternions by utilizing established properties of k ...
A. D. Godase
doaj   +1 more source

Elementary sequences, sub-Fibonacci sequences

Discrete Applied Mathematics, 1993
A nondecreasing integer sequence \(x_ 1,x_ 2,\dots,x_ k\) with \(x_ 1=x_ 2=1\) and \(n \geq 2\) is said to be elementary if for all \(k \leq n\) \((x_ k>1 \Rightarrow x_ k=x_ i+x_ j\) for some \(i \neq j)\) and sub- Fibonacci if for all \(k \in \{3,\dots,n\}\) \((x_ k \leq x_{k-1}+x_{k- 2})\).
Fishburn, Peter C., Roberts, Fred S.
openaire   +1 more source

Generalization of the Distance Fibonacci Sequences

Axioms
In this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties ...
Nur Şeyma Yilmaz, Andrej Włoch, Engin Özkan   +2 more
doaj   +1 more source

On a generalization of the Hosoya triangle [PDF]

Notes on Number Theory and Discrete Mathematics
This paper introduces the Fibonacci polynomial triangle, inspired by the structure of the Hosoya triangle and constructed using Fibonacci polynomials.
Turhan Çifçi, Hamza Menken, Orhan Dişkaya   +2 more
doaj   +1 more source

Another six Fibonacci-like sequences [PDF]

Notes on Number Theory and Discrete Mathematics
We briefly describe six Fibonacci-like sequences or arbitrary order that give rise to a periodic or eventually periodic sequences. We provide some examples and demonstrate the explicit periods of these sequences.
Karol Gryszka
doaj   +1 more source

Some sums related to the terms of generalized Fibonacci autocorrelation sequences

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2017
In this paper, we give the terms of the generalized Fibonacci autocorrelation sequences defined as and some interesting sums involving terms of these sequences for an odd integer number and nonnegative integers.
Neşe Ömür , Sibel Koparal
doaj   +1 more source

(±1)-Invariant sequences and truncated Fibonacci sequences

Linear Algebra and its Applications, 2005
Let \(P\) and \(D\) denote the Pascal matrix \(\bigl[\binom{i}{j}\bigr]\), (\(i,j=0,1,2,\dots\)) and the diagonal matrix \(\text{diag}((-1)^0,(-1)^1,(-1)^2,\dots)\), respectively. An infinite-dimensional real vector \(\mathbf x\) is called a \(\lambda\)-invariant sequence if \(PD\mathbf x=\lambda\mathbf x\).
Choi, Gyoung-Sik, Hwang, Suk-Geun, Kim, Ik-Pyo, Shader, Bryan L.   +3 more
openaire   +1 more source

Psychoacoustic Properties of Fibonacci Sequences

Acta Polytechnica, 2008
1202, Fibonacci set up one of the most interesting sequences in number theory. This sequence can be represented by so-called Fibonacci Numbers, and by a binary sequence of zeros and ones.
J. Sokoll, S. Fingerhuth
doaj