Results 11 to 20 of about 145 (136)

On r -Jacobsthal and r -Jacobsthal-Lucas Numbers

Annales Mathematicae Silesianae, 2023
Abstract Recently, Bród introduced a new Jacobsthal-type sequence which is called r -Jacobsthal sequence in current study. After defining the appropriate r -Jacobsthal–Lucas sequence for the r ...
Göksal Bilgici, Dorota Bród
openaire   +2 more sources

The Frobenius Number for Jacobsthal Triples Associated with Number of Solutions

Axioms, 2023
In this paper, we find a formula for the largest integer (p-Frobenius number) such that a linear equation of non-negative integer coefficients composed of a Jacobsthal triplet has at most p representations.
Takao Komatsu, Claudio Pita-Ruiz
doaj   +1 more source

Horadam Polynomials and a Class of Biunivalent Functions Defined by Ruscheweyh Operator

International Journal of Mathematics and Mathematical Sciences, Volume 2023, Issue 1, 2023., 2023
In this paper, we introduce and investigate a class of biunivalent functions, denoted by Hn,r,α, that depends on the Ruscheweyh operator and defined by means of Horadam polynomials. For functions in this class, we derive the estimations for the initial Taylor–Maclaurin coefficients |a2| and |a3|.
Waleed Al-Rawashdeh, Teodor Bulboaca
wiley   +1 more source

Dual Jacobsthal Quaternions

Communications in Advanced Mathematical Sciences, 2020
In this paper, dual Jacobsthal quaternions were defined. Also, the relations between dual Jacobsthal quaternions which connected with Jacobsthal and Jacobsthal-Lucas numbers were investigated. Furthermore, Binet's formula, Honsberger identity, D'ocagne'
Fügen Torunbalcı Aydın
doaj   +1 more source

The Complex‐Type k‐Pell Numbers and Their Applications

Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023
In this study, a new sequence called the complex‐type k‐Pell number is defined. Also, we give properties of this sequence such as the generating matrix, the generating function, the combinatorial representations, the exponential representation, the sums, the permanental and determinantal representations, and the Binet formula.
Yeşim Aküzüm, Xiaogang Liu
wiley   +1 more source

Solutions of the Diophantine Equations Br = Js + Jt and Cr = Js + Jt

Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023
Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br = Js + Jt and Cr = Js + Jt are completely solved. The solutions rely basically on Matveev’s theorem on linear forms in logarithms of algebraic numbers and a procedure of reducing the upper bound due to Dujella
Ahmed Gaber, Mohiedeen Ahmed, Xiaogang Liu   +2 more
wiley   +1 more source

On New Polynomial Sequences Constructed to Each Vertex in an n‐Gon

Discrete Dynamics in Nature and Society, Volume 2022, Issue 1, 2022., 2022
In this work, we bring to light the properties of newly formed polynomial sequences at each vertex of Pell polynomial sequences placed clockwise at each vertex in the n‐gon. We compute the relation among the polynomials with such vertices. Moreover, in an n‐gon, we generate a recurrence relation for a sequence giving the mth term formed at the kth ...
Abdul Hamid Ganie, Engin ŏzkan, Mine Uysal, Afroza Akhter, Ya Jia   +4 more
wiley   +1 more source

Generalized commutative Jacobsthal quaternions and some matrices

Examples and Counterexamples, 2023
In this paper, some examples of matrix generators for generalized commutative Jacobsthal quaternions were given. The generating matrices are useful tools for the number sequences satisfying a recurrence relation.
Dorota Bród, Anetta Szynal-Liana
doaj   +1 more source

A New Method of Matrix Decomposition to Get the Determinants and Inverses of r‐Circulant Matrices with Fibonacci and Lucas Numbers

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
We use a new method of matrix decomposition for r‐circulant matrix to get the determinants of An = Circr(F1, F2, …, Fn) and Bn = Circr(L1, L2, …, Ln), where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived.
Jiangming Ma, Tao Qiu, Chengyuan He, Firdous A. Shah   +3 more
wiley   +1 more source