Results 11 to 20 of about 1,148,545 (158)

New results for the Fibonacci sequence using Binet's formula

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

On the Products of k-Fibonacci Numbers and k-Lucas Numbers [PDF]

International Journal of Mathematics and Mathematical Sciences, 2014
In this paper we investigate some products of k-Fibonacci and k-Lucas numbers. We also present some generalized identities on the products of k-Fibonacci and k-Lucas numbers to establish connection formulas between them with the help of Binet's formula.
Bijendra Singh, Kiran Sisodiya, Farooq Ahmad   +2 more
doaj   +2 more sources

On the Lichtenberg hybrid quaternions [PDF]

Mathematica Moravica
In this study, we define Lichtenberg hybrid quaternions. We give the Binet's formula, the generating functions, exponential generating functions and sum formulas of these quaternions. We find some relations between Jacobsthal hybrid quaternions, Mersenne
Morales Gamaliel
doaj   +2 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

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   +4 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

Dirichlet Convolution and the Binet Formula

, 2023
Summary: The main aim of this note is to show that the set of closed triples of generalized Fibonacci arithmetic functions under the Dirichlet convolution is a singleton set. This unique Dirichlet convolution identity is the Binet Fibonacci number formula in terms of arithmetic functions and the Dirichlet convolution.
Schwab, Emil Daniel, Schwab, Gabriela
openaire   +2 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