Results 71 to 80 of about 616 (205)

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

The p-adic valuation of Lucas sequences [PDF]

, 2016
Let (un)n≥0 be a nondegenerate Lucas sequence with characteristic polynomial X2 − aX − b, for some relatively prime integers a and b. For each prime number p and each positive integer n, we give simple formulas for the p-adic valuation νp(un), in terms ...
Sanna, Carlo
core  

A trick around Fibonacci, Lucas and Chebyshev [PDF]

, 2014
23 pagesInternational audienceIn this article, we present a trick around Fibonacci numbers which can be found in several magic books. It consists in computing quickly the sum of the successive terms of a Fibonacci-like sequence.
Lachal, Aimé
core   +8 more sources

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

Multiplicative dependence of k-Fibonacci numbers with the Fibonacci, Lucas, and Pell sequences

The Ramanujan Journal
Abstract The k –generalized Fibonacci sequence $$(F_m^{(k)})_{m\ge 2-k}$$ (
Gómez, C, C. Gómez, J, Luca, F
openaire   +2 more sources

Bi-periodic Fibonacci and Lucas matrix sequences [PDF]

, 2019
Son yıllarda, bilim dünyasının ilgisini çeken ve birçok alanda karşımıza çıkan Fibonacci, Lucas, Pell, Pell-Lucas, -Fibonacci ve -Lucas sayı dizileri ile ilgili pek çok çalışma vardır.
Coşkun, Arzu
core  

The sequences of Fibonacci and Lucas for quadratic fields

Boletim da Sociedade Paranaense de Matemática
We construct the sequences of Fibonacci and Lucas in any quadratic field $\mathbb{Q}(\sqrt{d}\,)$ with $d>0$ square free, noting that the general properties remain valid as those given by the classical sequences of Fibonacci and Lucas for the case $d = 5$, under the respective variants.
Pablo Lam-Estrada, Myrian Rosalia Maldonado-Ramirez, Jose Luis Lopez-Bonilla, Fausto Jarquin Zarate, R. Rajendra, Siva Kota Reddy Polaepalli   +5 more
openaire   +1 more source

Unique Properties of the Fibonacci and Lucas Sequences [PDF]

, 2017
The algebraic structure of the set of all Fibonacci-like sequences, which includes the Fibonacci and Lucas sequences, is developed, utilizing an isomorphism between this set and a subset of the 2 by 2 integer matrices.
Parry, Stephen
core   +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

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