Results 81 to 90 of about 159 (139)

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
doaj   +1 more source

Generalized Jacobsthal-Narayana Numbers and Generalized Co-Jacobsthal-Narayana Numbers

Asian Journal of Advanced Research and Reports
This paper introduces two innovative third-order recurrence sequences: the generalized Jacobsthal-Narayana sequence and the co-Jacobsthal-Narayana sequence. It examines their interrelated properties, including Binet’s formulas, generating functions, Simson’s formulas, and matrix representations, as well as their special subsequences.
openaire   +1 more source

Integral representations of the Jacobsthal and Jacobsthal-Lucas numbers

Our study aims to obtain integral representations of Jacobsthal J_kn and Jacobsthal-Lucas L_kn, and then to use these integral representations to derive integral representations of Jacobsthal J_kn+r and Jacobsthal-Lucas L_kn+r, where n\in Z_0={0,1,2,..} is a non-negative integer, k \in Z_>0=1,2,3,...  is an arbitrary but fixed positive integer, while r
openaire   +2 more sources

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Admixture Models and the Breeding Systems of H. S. Jennings: A GENETICS Connection. [PDF]

Genetics, 2016
Rosenberg NA.
europepmc   +1 more source

Non-Newtonian Jacobsthal and Jacobsthal-Lucas numbers: A new look

Filomat
In this study, we introduce a novel version of Jacobsthal and Jacobsthal-Lucas numbers, termed as non-Newtonian Jacobsthal and non-Newtonian Jacobsthal-Lucas numbers. We investigate various char-acteristics of these newly defined sequences. Additionally, we explore several formulas and identities such as Cassini?s identity, d?Ocagne?s identity, Binet?s
İlknur Yeşilyurt, Nilay Değirmen
openaire   +1 more source

Beyond 2/3 and 1/3: The Complex Signatures of Sex-Biased Admixture on the X Chromosome. [PDF]

Genetics, 2015
Goldberg A, Rosenberg NA.
europepmc   +1 more source