Zobrazeno 1 - 10
of 182
pro vyhledávání: '"11B37, 11B39"'
Autor:
Wojtkowski, Maciej P.
We propose a new interpretation of the classical index of appearance for second order linear recursive sequences. It stems from the formula \[ C_{n}(t)-2 =\frac{\Delta}{Q^{n}}\ L_n^2,\ \ \ \text{where} \ \ t= (T^2-2Q)/Q, \ \Delta = T^2-4Q, \] connect
Externí odkaz:
http://arxiv.org/abs/2410.22831
Autor:
Bruda, Glenn, Fang, Bruce, Gilman, Pico, Marquez, Raul, Miller, Steven J., Prapashtica, Beni, Son, Daeyoung, Waheed, Saad, Wang, Janine
Motivated by the rich properties and various applications of recurrence relations, we consider the extension of traditional recurrence relations to matrices, where we use matrix multiplication and the Kronecker product to construct matrix sequences.
Externí odkaz:
http://arxiv.org/abs/2408.12660
Let $Q$ be the matrix $\displaystyle \begin{pmatrix} a & b \\ 1 & 0 \end{pmatrix}$ in $GL_2(\mathbb{F}_q)$ where $\mathbb{F}_q$ is a finite field, and let $G$ be the finite cyclic group generated by $Q$. We consider the action of $G$ on the set $\mat
Externí odkaz:
http://arxiv.org/abs/2408.09561
Autor:
Anand, Navvye, Basistha, Amit Kumar, Davenport, Kenny B., Gong, Alexander, Miller, Steven J., Zhu, Alexander
We study new identities related to the sums of adjacent terms in the Pell sequence, defined by $P_{n} := 2P_{n-1}+P_{n-2}$ for $ n\geq 2$ and $P_{0}=0, P_{1}=1$, and generalize these identities for many similar sequences. We prove that the sum of $N>
Externí odkaz:
http://arxiv.org/abs/2407.12868
Autor:
Pérez-Rosés, Hebert
The change-making problem consists of representing a certain amount of money with the least possible number of coins, from a given, pre-established set of denominations. The greedy algorithm works by choosing the coins of largest possible denominatio
Externí odkaz:
http://arxiv.org/abs/2405.16609
We evaluate in closed form several alternating infinite series involving the binomial coefficients $C(4n,2n)$ and $C(4n+2,2n+1)$ in the denominator. One of our results generalizes an identity that was obtained experimentally by Sprugnoli in 2006.
Externí odkaz:
http://arxiv.org/abs/2404.05770
Autor:
Cerda-Morales, Gamaliel
In this paper, a new generalization of third-order Jacobsthal bihyperbolic polynomials is introduced. Some of the properties of presented polynomials are given. A Vadja formula for the generalized bihyperbolic third-order Jacobsthal polynomials is ob
Externí odkaz:
http://arxiv.org/abs/2404.05738
Autor:
Frontczak, Robert, Gryszka, Karol
In this paper, using a generating function approach, we derive several new convolution sum identities involving Fibonacci m-step numbers. As special instances of the results derived herein, we will get many new and known results involving Fibonacci,
Externí odkaz:
http://arxiv.org/abs/2403.19701
Autor:
Savin, Diana, Tan, Elif
In this paper, we introduce a new class of quaternions called Lucas-Leonardo p-quaternions and derive several fundamental properties of these numbers. Furthermore, we investigate some applications related to companion sequences associated with Leonar
Externí odkaz:
http://arxiv.org/abs/2403.01592
Autor:
Voutier, Paul M
We investigate the number of squares in a very broad family of binary recurrence sequences with $u_{0}=1$. We show that there are at most two distinct squares in such sequences (the best possible result), except under such very special conditions whe
Externí odkaz:
http://arxiv.org/abs/2401.01293