论文标题
关于$（q，k）$ - 概括的斐波那契数字的序列
On the Sequences of $(q,k)$-Generalized Fibonacci Numbers
论文作者
论文摘要
在本文中，我们考虑了$（q，k）$概括的斐波那契数的新系列。这些序列自然扩展了$ K $笼统的斐波那契数和广义$ k $ order-rorder pell数字的众所周知的序列。我们将获得Binet式公式，并研究特征方程式主要根的渐近行为。此外，我们将证明有关这些序列的一些辅助结果。特别是，我们在二进制序列方面表征了第一个$（q，k）$的斐波那契数。
In this paper, we consider the new family of recurrence sequences of $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers. We shall obtain a Binet-style formula and study the asymptotic behavior of dominant root of characteristic equation. Moreover, we shall prove some auxiliary results about these sequences. In particular, we characterize the first $(q,k)$-generalized Fibonacci numbers in terms of binary sequences.
