Results 31 to 40 of about 427,829 (170)
The Solution of a System of Higher-Order Difference Equations in Terms of Balancing Numbers
Pan-American Journal of Mathematics, 2023 In this paper, we are interested in the closed-form solution of the following system of nonlinear difference equations of higher order, un+1 = 1/34-vn-m , vn+1 = 1/34-un-m, n, m ∈ N0, and the initial values u-j and v-j , j∈{0, 1, ..., m} are real numbers
Ahmed Ghezal, Imane Zemmouri
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Exact divisibility by powers of the integers in the Lucas sequence of the first kind
AIMS Mathematics, 2020 Lucas sequence of the first kind is an integer sequence $(U_n)_{n\geq0}$ which depends on parameters $a,b\in\mathbb{Z}$ and is defined by the recurrence relation $U_0=0$, $U_1=1$, and $U_n=aU_{n-1}+bU_{n-2}$ for $n\geq2$. In this article, we obtain exact
Kritkhajohn Onphaeng +1 more
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Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras
Discussiones Mathematicae - General Algebra and Applications, 2021 The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation.
Patra Asim
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Solutions of the Diophantine Equations Br=Js+Jt and Cr=Js+Jt
Journal of Mathematics, 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.
Ahmed Gaber, Mohiedeen Ahmed
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On Balancing Quaternions and Lucas-Balancing Quaternions
Discussiones Mathematicae - General Algebra and Applications, 2021 In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have
Bród Dorota
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Journal of Innovative Applied Mathematics and Computational Sciences, 2021 In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.
Yüksel Soykan +2 more
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Greatest common divisors of shifted balancing numbers
Boletim da Sociedade Paranaense de Matemática, 2017 It is well known that the successive balancing numbers are relatively prime. Let for all integers a, sn(a) denotes the greatest common divisor of the shifted balancing numbers of the form sn(a) = gcd(Bn a; Bn+1 6a).
Prasanta Kumar Ray
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Mersenne-Horadam identities using generating functions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
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Relation between the correspondence chromatic number and the Alon--Tarsi number [PDF]
arXiv, 2022 We study the relation between the correspondence chromatic number and the Alon--Tarsi number, both upper bounds on the list chromatic number of a graph. There are many graphs with Alon--Tarsi number greater than the correspondence chromatic number.
arxiv
On some properties of polycosecant numbers and polycotangent numbers [PDF]
arXiv, 2022 Polycosecant numbers and polycotangent numbers are introduced as level two analogues of poly-Bernoulli numbers. It is shown that polycosecant numbers and polycotangent numbers satisfy many formulas similar to those of poly-Bernoulli numbers. However, there is much unknown about polycotangent numbers. For example, the zeta function interpolating them at
arxiv