Results 51 to 60 of about 3,822 (183)

Generating matrix of the bi-periodic Lucas numbers

, 2016
In this paper, firstly, we introduce the Q_{l}-Generating matrix for the bi-periodic Lucas numbers. Then, by taking into account this matrix representation, we obtain some properties for the bi-periodic Fibonacci and Lucas ...
Coskun, Arzu, Taskara, Necati
core   +1 more source

A Generalization of Gaussian Balancing and Gaussian Balancing‐Lucas Numbers With Applications

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
In this paper, we study a generalization of Gaussian balancing and Gaussian Lucas‐balancing numbers, we find their generating functions, Binet formulas, related matrix representation, and many other properties. Also, we provide some applications in cryptography.
T. Al-Asoully, A. Al-Kateeb, Abdul Rauf Khan   +2 more
wiley   +1 more source

Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers

Journal of Mathematics, 2023
In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
doaj   +1 more source

Some results on average of Fibonacci and Lucas sequences

, 2020
In this paper, we discuss about some results on average of Fibonacci and Lucas sequences that may be found in the OEIS code A111035.
Yaqubi, Daniel, Fatehizadeh, Amirali
openaire   +2 more sources

Computational Framework for Numerical Simulation of Fractional‐Order Financial Crime Model via Lucas Collocation Technique

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
The Lucas collocation approach is used in this study to approximate a fractional‐order financial crime model (FOFCM) numerically. The model categorizes the population into five groups: persons without a financial criminal past, those inclined toward financial crimes, active participants, individuals undergoing prosecution, and those imprisoned.
Mahmoud Abd El-Hady, Homan Emadifar, Mehdi Hariri, Atallah El-Shenawy, Chong Lin   +4 more
wiley   +1 more source

Free Fibonacci Sequences [PDF]

, 2014
This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: given n, sum the previous two terms and divide them by the largest possible power of n. The behavior of such sequences depends on n.
Avila, Brandon, Khovanova, Tanya
core  

Split Quaternionic Representations of Horadam Sequences and Their Binet, Generating Function, and Cassini‐Type Identities

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study establishes a novel algebraic connection between Horadam numbers and the split quaternion algebra. To this end, two fundamental constructs are introduced: the Fibonacci Sq,r‐split quaternions and the Horadam sq,r‐split quaternions, which generalize Horadam numbers within the framework of split quaternions.
İskender Öztürk, Hasan Çakır, Smritijit Sen   +2 more
wiley   +1 more source

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

On Some Properties of Tribonacci Quaternions

, 2017
In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for ...
Akkus, Ilker, Kizilaslan, Gonca
core   +1 more source