Results 21 to 30 of about 11,331 (154)

On Sums of Squares of Pell-Lucas Numbers

Integers, 2006
In this paper we prove several formulas for sums of squares of even Pell-Lucas numbers, sums of squares of odd Pell-Lucas numbers, and sums of products of even and odd PellLucas numbers. These sums have nice representations as products of appropriate Pell and Pell-Lucas numbers with terms from certain integer sequences.
Čerin, Zvonko, Gianella, Gian Mario
openaire   +4 more sources

Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials

Discrete Dynamics in Nature and Society, 2012
We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci, Mirac Cetin Firengiz, Naim Tuglu   +2 more
doaj   +1 more source

Diophantine equations for additive Pell numbers in Pell, Pell–Lucas, and Modified Pell numbers [PDF]

Notes on Number Theory and Discrete Mathematics
This paper investigates the Diophantine equations arising from ternary additive problems of Pell, Pell-Lucas, and Modified Pell numbers. Specifically, we characterize all integer solutions to the equation Pₙ+Pₘ+Pᵣ=Xₖ, X∈{P,Q,R}, where Pᵢ, Qᵢ, and Rᵢ ...
Ahmet Emin, Ahmet Daşdemir
doaj   +1 more source

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
doaj   +1 more source

Non-Fisherian generalized Fibonacci numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Using biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
doaj   +1 more source

Tribonacci and Tribonacci-Lucas Sedenions

, 2018
The sedenions form a 16-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tribonacci and Tribonacci-Lucas sedenions. Furthermore, we present some properties of these sedenions and derive relationships between them.Comment: 17 pages, 1 ...
Soykan, Yüksel
core   +1 more source

Gaussian Generalized Tetranacci Numbers

, 2019
In this paper, we define Gaussian generalized Tetranacci numbers and as special cases, we investigate Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers with their ...
Soykan, Yüksel
core   +1 more source

Diophantine tuples and product sets in shifted powers

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley   +1 more source

Acoustic Features of Emotional Vocalizations Account for Early Modulations of Event‐Related Brain Potentials

Psychophysiology, Volume 63, Issue 2, February 2026.
ABSTRACT Emotion is key to human communication, and inferring emotion in a speaker's voice is a cross‐cultural and cross‐linguistic capability. Electroencephalography (EEG) studies of neural mechanisms supporting emotion perception have reported that early components of the event‐related potential (ERP) are modulated by emotion.
Yichen Tang, Paul M. Corballis, Luke E. Hallum   +2 more
wiley   +1 more source

On the Balancing-bilinear system of difference equations: solutions via some number sequences and global stability

Miskolc Mathematical Notes
In the current paper, we present a new class of systems called the Balancing-bilinear system of difference equations to investigate some theoretical proprieties.
Ahmed Ghezal, Imane Zemmouri
doaj   +1 more source