On the (r, p, k)-Generalized Jacobsthal Numbers and the Jacobsthal Fundamental Fibonacci System
Trends in Computational and Applied MathematicsThe main goal of this paper is to study the model of the sequences of (r, p, k)-generalized Jacobsthal numbers, by the approach based on the properties of its associated Jacobsthal fundamental Fibonacci system and its fundamental sequence. Some linear and combinatorial properties are established.
RACHIDI, M., YILMAZ, F.
openaire +4 more sources
New families of Jacobsthal and Jacobsthal-Lucas numbers
, 2015 In this paper we present new families of sequences that generalize the Jacobsthal and the Jacobsthal-Lucas numbers and establish some identities. We also give a generating function for a particular case of the sequences presented.
Campos, Helena +4 more
openaire +3 more sources
On the bi-periodic k-Jacobsthal and k-Jacobsthal-Lucas numbers
Progress in Applied Science and TechnologyThis paper introduces and investigates the bi-periodic Jacobsthal and Jacobsthal–Lucas sequences, extending the classical Jacobsthal framework by incorporating periodicity and a tunable parameter . We establish recurrence relations, derive generating functions, and present Binet-type formulas for these generalized sequences.
Mongkol Tatong, Oam Sthityanak
openaire +1 more source
Common Factors of Generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers
International Journal of Applied Mathematical Research, 2012 In this paper, we present identities involving common factors of generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers. Binet’s formula will employ to obtain the identities.
V. K. Gupta, Yashwant Kumar Panwar
openaire +2 more sources
On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers
Journal of Engineering Technology and Applied Sciences, 2019 In this study, we compute the value of the various norms of the Toeplitz matrices whose elements are Jacobsthal numbers, Jacobsthal Lucas numbers and upper and lower bounds for the spectral norms of these matrices. Also, the Euclidean norm of Kronecker product of Toeplitz matrices with Jacobsthal and the Jacobsthal Lucas numbers are denoted.
openaire +3 more sources
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
Generalized Jacobsthal-Narayana Numbers and Generalized Co-Jacobsthal-Narayana Numbers
Asian Journal of Advanced Research and ReportsThis 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
Non-Newtonian Jacobsthal and Jacobsthal-Lucas numbers: A new look
FilomatIn 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
Admixture Models and the Breeding Systems of H. S. Jennings: A GENETICS Connection. [PDF]
Genetics, 2016 Rosenberg NA.
europepmc +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