Results 71 to 80 of about 1,421 (176)
, 2023 We consider the greatest common divisor (GCD) of all sums of $k$ consecutive terms of a sequence $(S_n)_{n\geq 0}$ where the terms $S_n$ come from exactly one of following six well-known sequences' terms: Pell $P_n$, associated Pell $Q_n$, balancing $B_n$, Lucas-balancing $C_n$, cobalancing $b_n$, and Lucas-cobalancing $c_n$ numbers.
Mbirika, Aba +2 more
openaire +3 more sources
On some properties of k-circulant matrices with the generalized Pell-Padovan numbers
Journal of Innovative Applied Mathematics and Computational SciencesIn this paper, we investigate the properties of the $k$-circulant matrix generated by the generalized Pell--Padovan numbers. We derive explicit formulas for the sum of entries, the maximum column sum norm ($\Vert \cdot \Vert _{1}$), the maximum row sum ...
Yüksel Soykan, Erkan Taşdemir
doaj +1 more source
Common values of two k-generalized Pell sequences [PDF]
Notes on Number Theory and Discrete MathematicsLet k≥2 and let (Pₙ⁽ᵏ⁾)ₙ≥₂₋ₖ be the k-generalized Pell sequence defined by Pₙ⁽ᵏ⁾=2Pₙ₋₁⁽ᵏ⁾+2Pₙ₋₂⁽ᵏ⁾+...+2Pₙ₋ₖ⁽ᵏ⁾ for n≥2 with initial conditions P₋₍ₖ₋₂₎⁽ᵏ⁾=P₋₍ₖ₋₃₎⁽ᵏ⁾=...=P₋₁⁽ᵏ⁾=P₀⁽ᵏ⁾=0, and P₁⁽ᵏ⁾=1.
Zafer Şiar +2 more
doaj +1 more source
Tridiagonal matrices representations of generalized bivariate complex polynomials
Journal of Innovative Applied Mathematics and Computational SciencesThis paper introduces a closed-form expression for generalized bivariate complex polynomials using a tridiagonal determinant in symbolic form. Subsequences with even and odd indices are also represented as tridiagonal determinants.
K. L. Verma
doaj +1 more source
Complex Dynamics of Pell Sequence
International Journal of Computer Applications, 2010 Binet formula for Pell sequence is viewed as a function of complex variable. In this paper the study of attracting and repelling fixed points of Pell sequence is presented with the complex dynamics resulting in the escape time images. A study of orbits of the Binet type formula is presented in the paper.
Rajeshri Rana +2 more
openaire +1 more source
On q-Pell sequence spaces: A study of operator ideals and geometric properties
Kuwait Journal of ScienceThe matrix \( \mathcal{P}(q) = \{\Psi_{\lambda \mu}(q)\}_{\lambda, \mu \in \mathbb{N}} \), called the \( q \)-Pell matrix, with elements determined by \[ \mathcal{P}(q) = \begin{cases} \dfrac{2~q^{\mu-1}~\Psi{_\mu(q)}}{\Psi{_{\lambda+1}(q)}+\Psi{_ ...
Shiva Shah, Bipan Hazarika
doaj +1 more source
Miskolc Mathematical NotesIn 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
On the sequences of $(q,k)$-generalized Fibonacci numbers [PDF]
Mathematica BohemicaWe consider a new family of recurrence sequences, the $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers.
Jean Lelis +3 more
doaj +1 more source
A Hybrid Matrix-Based Cryptographic Framework Using Multiple Linear Recurrence Sequences
MathematicsIn this study, we propose a matrix-based transformation framework constructed from special integer sequences, including Fibonacci, Lucas, Pell, and Jacobsthal numbers.
Sukran Uygun
doaj +1 more source
On the Domain of the Pell-Lucas Matrix in the Spaces c and c_0
Dera Natung Government College Research JournalIn this study, we introduce new Banach sequence spaces $c(\Theta), c_0(\Theta)$, defined via a regular infinite matrix $ \Theta = (\lambda_{nk})$, where \[ \Theta_{nk} = \begin{cases} \dfrac{2\lambda_k}{3\lambda_n+\lambda_{n-1}} & 0 \leq k \leq n ...
Shiva Shah
doaj +1 more source