Results 1 to 10 of about 1,240,504 (163)

Binomial Transforms of the Third-Order Jacobsthal and Modified Third-Order Jacobsthal Polynomials

Universal Journal of Mathematics and Applications
In this study, we define the binomial transforms of third-order Jacobsthal and modified third-order Jacobsthal polynomials. Further, the generating functions, Binet formulas and summation of these binomial transforms are found by recurrence relations ...
Gamaliel Morales
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On ̄h-Jacobsthal and ̄h-Jacobsthal–Lucas sequences, and related quaternions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
In this paper, inspired by recent articles of A. Szynal-Liana & I. Włoch and F. T. Aydin & S. Yüce (see [26] and [2]), we will introduce the ̄h-Jacobsthal quaternions and the ̄h-Jacobsthal–Lucas sequences and their associated quaternions. The new results
Anatriello Giuseppina, Vincenzi Giovanni
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The nth Power of Generalized (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Matrix Sequences and Some Combinatorial Properties

Journal of New Theory, 2021
In this study, new formulas for the nth power of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas special matrix sequences are established by using determinant and trace of the matrices.
Şükran Uygun
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Some results on one type of graph family with some special number sequences

AKCE International Journal of Graphs and Combinatorics, 2020
In this study, we introduce a new graph family. Then, we calculate eigenvalues of the adjacency and the Laplacian matrix of this graph family. Moreover, we show that the perfect matching number of this graph family equals to special second order ...
Emrullah Kirklar, A. Dilek Maden, Fatih Yilmaz   +2 more
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Fermatian row and column sums as a family of generalized integers [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we introduce some feature of the Fermatian numbers. The finite sum formulas of these numbers is calculate. The exponential generating function of Fermatian numbers is found and some of its identities is calculated.
Anthony G. Shannon, Mine Uysal, Engin Özkan   +2 more
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On (k1A1, k2A2, k3A3)-Edge Colourings in Graphs and Generalized Jacobsthal Numbers

Annales Mathematicae Silesianae
In this paper we introduce a new kind of generalized Jacobsthal numbers in a distance sense. We give the identities and matrix representations for them and their connections with the Fibonacci and the Pell numbers. We also describe the interpretations of
Piejko Krzysztof, Trojnar-Spelina Lucyna
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Relations Established Between Hypergeometric Functions and Some Special Number Sequences

Axioms
In this paper, we establish new hypergeometric representations for two classical integer sequences, namely the Pell and Jacobsthal sequences. Motivated by Dilcher’s hypergeometric formulations of the Fibonacci sequence, we extend this framework to other ...
Sukran Uygun, Berna Aksu, Hulya Aytar
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Novel Classes on Generating Functions of the Products of (p,q)-Modified Pell Numbers with Several Bivariate Polynomials

Mathematics
In this paper, using the symmetrizing operator δe1e22−l, we derive new generating functions of the products of p,q-modified Pell numbers with various bivariate polynomials, including Mersenne and Mersenne Lucas polynomials, Fibonacci and Lucas ...
Ali Boussayoud, Salah Boulaaras, Ali Allahem   +2 more
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Sums of generalized third-order Jacobsthal numbers by matrix methods

Trends in Computational and Applied Mathematics
In this paper, we consider a certain third-order linear recurrence and then give generating matrices for the sums of positively and negatively subscripted terms of this recurrence.
G. Cerda-Morales
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A Note on Generalized k-Order F&L Hybrinomials

Axioms
In this study, we introduce generalized k-order Fibonacci and Lucas (F&L) polynomials that allow the derivation of well-known polynomial and integer sequences such as the sequences of k-order Pell polynomials, k-order Jacobsthal polynomials and k-order ...
Süleyman Aydınyüz, Gül Karadeniz Gözeri   +1 more
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