Results 41 to 50 of about 187 (159)

A Note on Stability of a Linear Functional Equation of Second Order Connected with the Fibonacci Numbers and Lucas Sequences

Journal of Inequalities and Applications, 2010
We prove the Hyers-Ulam stability of a second-order linear functional equation in single variable (with constant coefficients) that is connected with the Fibonacci numbers and Lucas sequences.
Janusz Brzdęk, Soon-Mo Jung
doaj   +2 more sources

Generalized Bronze Leonardo sequence [PDF]

Notes on Number Theory and Discrete Mathematics
In this study, we define the Bronze Leonardo, Bronze Leonardo–Lucas, and Modified Bronze Leonardo sequences, and some terms of these sequences are given. Then, we give special summation formulas, special generating functions, etc.
Engin Özkan, Hakan Akkuş
doaj   +1 more source

Fibonacci and k Lucas Sequences as Series of Fractions

Mathematical Journal of Interdisciplinary Sciences, 2016
In this paper, we defined new relationship between k Fibonacci and k Lucas sequences using continued fractions and series of fractions, this approach is different and never tried in k Fibonacci sequence literature.
A. D. Godase, M. B. Dhakne
openaire   +1 more source

Properties of Generalized Bronze Fibonacci Sequences and Their Hyperbolic Quaternions

Axioms
In this study, we establish some properties of Bronze Fibonacci and Bronze Lucas sequences. Then we find the relationships between the roots of the characteristic equation of these sequences with these sequences.
Engin Özkan, Hakan Akkuş, Alkan Özkan
doaj   +1 more source

Fibonacci Cartan and Lucas Cartan numbers

Open Mathematics
This study introduces Fibonacci Cartan and Lucas Cartan numbers, extending the classical Fibonacci and Lucas sequences into the framework of Cartan numbers.
Öztürk İskender, Çakır Hasan
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The Third Order Jacobsthal Octonions: Some Combinatorial Properties

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways.
Cerda-Morales Gamaliel
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On the Periods of Biperiodic Fibonacci and Biperiodic Lucas Numbers

Discrete Dynamics in Nature and Society, 2016
This paper is concerned with periods of Biperiodic Fibonacci and Biperiodic Lucas sequences taken as modulo prime and prime power. By using Fermat’s little theorem, quadratic reciprocity, many results are obtained.
Dursun Tascı, Gul Ozkan Kızılırmak
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A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
Bahar Kuloğlu
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On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods [PDF]

International Journal of Mathematical Sciences and Computing, 2017
In the present paper first and foremost we introduce a generalization of a classical Fibonacci sequence which is known as Fibonacci-Like sequence and at hindmost we obtain some relationships between Lucas sequence and Fibonacci-Like sequence by using two cross two matrix representation to the Fibonacci-Like sequence.
Arfat Ahmad Wani, V. H. Badshah
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Fibonacci and Lucas sequences at negative indices

, 2014
This study investigate the Fibonacci and Lucas sequences at neg- ative indices. In this paper we give the formulas of F????(nk+r) and L????(nk+r) depending on whether the indices are odd or even. For this purpose we con- sider a special matrix and we give various combinatorial identities related with the Fibonacci and Lucas sequences by using the ...
Halıcı, Serpil, Akyüz, Zeynep
openaire   +3 more sources