Results 11 to 20 of about 1,044,414 (185)

New results for the Fibonacci sequence using Binet's formula

International Mathematical Forum, 2018
Reza Farhadian, Rafael Jakimczuk
semanticscholar   +3 more sources

A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Journal of Mathematics
In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1.
Hasan Gökbaş
doaj   +2 more sources

Exploring Generalized $2^k$-Fibonacci Sequence: A New Family of the Fibonacci Sequence

Communications in Advanced Mathematical Sciences
The focus of this paper is to study the $2^k$–Fibonacci sequence, which is defined for all integers $2^k$, and its connections with both the Fibonacci and the Fibonacci-Lucas sequences.
Elis Gardel Costa Mesquista, Eudes Antonio Costa, Paula Maria Machado Cruz Catarino   +2 more
doaj   +2 more sources

On an application of Binet’s second formula

Proceedings of the American Mathematical Society, 2017
Let \(f(x)= \int^\infty_0 ((\sin t)/(t+ x))\,dt\) and \(g(x)= \int^\infty_0 ((\cos t)/(t+ x))\,dt\). The author proves the following representation formulas: \[ \begin{aligned} f(2\pi) &= \pi \sum^\infty_{n=1} {\mu(n)\over n}\,\Biggl(\log\Gamma(nx)- nx\log(nx)+ nx-{1\over 2}\log\Biggl({2\pi\over nx}\Biggr)\Biggr)\qquad\text{and}\\ g(2\pi) &= {1\over 2}\
Ruiming Zhang
semanticscholar   +2 more sources

Multiparameter Quantum Cauchy-Binet Formulas [PDF]

Algebras and Representation Theory, 2020
The quantum Cayley-Hamilton theorem for the generator of the reflection equation algebra has been proven by Pyatov and Saponov, with explicit formulas for the coefficients in the Cayley-Hamilton formula. However, these formulas do not give an \emph{easy} way to compute these coefficients.
Karlin, Samuel, Rinott, Yosef
  +8 more sources

Some properties and extended Binet’s formula for the class of bifurcating Fibonacci sequence

Ratio Mathematica
One of the generalizations of Fibonacci sequence is a -Fibonacci sequence, which is further generalized in several other ways, some by conserving the initial conditions and others by conserving the related recurrence relation.
Daksha Manojbhai Diwan, Devbhadra V Shah, Vandana R Patel   +2 more
doaj   +2 more sources

Elliptic curve and k-Fibonacci-like sequence

Scientific African, 2023
In this paper, we will introduce a modified k-Fibonacci-like sequence defined on an elliptic curve and prove Binet’s formula for this sequence. Moreover, we give a new encryption scheme using this sequence.
Zakariae Cheddour, Abdelhakim Chillali, Ali Mouhib   +2 more
doaj   +1 more source

The generalized Binet formula for $k$-bonacci numbers

Elemente der Mathematik, 2023
Using Vandermonde determinants, we give a simple proof of the generalization of the Binet formula to the k -bonacci numbers.
Parks, Harold R., Wills, Dean C.
openaire   +1 more source

Algorithm for Constructing an Analogue of the Binet Formula [PDF]

Programming and Computer Software, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuzovatov, V. I., Kytmanov, A. A., Kuzovatova, O. I.   +2 more
openaire   +3 more sources

Hybrid Quaternions of Leonardo

Trends in Computational and Applied Mathematics, 2022
In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented.
M. C. S. Mangueira, F. R. V. Alves, P. M. M. C. Catarino   +2 more
doaj   +1 more source