Results 71 to 80 of about 613 (205)

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

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

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

Narayana Numbers With Zeckendorf Partition in Two Terms

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The Narayan’s cow sequence starts with the terms 1, 1, and 1. Each subsequent term is obtained as the sum of the previous term and the term three places before. A term of this sequence is called a Narayana number. The mathematician Zeckendorf proved that every positive integer has a unique decomposition into a sum of distinct and nonconsecutive ...
Japhet Odjoumani, Salifou Nikiema, Shikha Binwal   +2 more
wiley   +1 more source

New generalizations of Fibonacci and Lucas sequences

Applied Mathematical Sciences, 2014
We consider the sequences { } and { } which are generated by the recurrence relations ( ) and ( ) with the initial conditions and where a and b are any non – zero real numbers. We obtain generating functions, Binet formulas for these two sequences and give generalizations of some well – known identities.
openaire   +1 more source

Bi‐Starlike Function of Complex Order Involving Rabotnov Function Associated With Telephone Numbers

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Telephone numbers defined through the recurrence relation Qn=Qn−1+n−1Qn−2 for n ≥ 2, with initial values of Q0=Q1=1. The study of such numbers has led to the establishment of various classes of analytic functions associated with them. In this paper, we establish two new subclasses of bi‐convex and bi‐starlike functions of complex order in the open unit
Sa’ud Al-Sa’di, Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Ming-Sheng Liu   +3 more
wiley   +1 more source

On the Existence of Solutions of Diophantine Equations Related to Subbalancing Numbers

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, we introduce a new sequence of subbalancing numbers by considering balancing numbers as the values of D in the Diophantine equations provided by subbalancing numbers. For this, first we prove that when the values of the positive integer D are chosen as balancing numbers, there exist integer solutions of the Diophantine equations that ...
Selin Sarı, Gül Karadeniz-Gözeri, Pramita Mishra   +2 more
wiley   +1 more source

A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Journal of Mathematics, Volume 2025, Issue 1, 2025.
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. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a ...
Hasan Gökbaş, Mohammad W. Alomari
wiley   +1 more source

Q-Analogues of biperiodic fibonacci and lucas sedenions [PDF]

, 2021
Quantum calculus has an important areas in many areas such as number theory, physics and mathematics. In this paper, by taking some useful notations from quantum calculus, we define the biperiodic Fibonacci and Lucas sedenions based on a q-parameter ...
Köme, Sure, Gün, Hafize
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