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The Log-Behavior of Ménage Numbers
Results in Mathematics ( IF 1.1 ) Pub Date : 2021-07-16 , DOI: 10.1007/s00025-021-01468-5
Yu-Xin Gu 1 , Feng-Zhen Zhao 1
Affiliation  

Let \(\{U_n\}_{n\ge 0}\) and \(\{V_n\}_{n\ge 0}\) denote the sequence of ordinary ménage numbers and the sequence of straight ménage numbers respectively. In this paper, we mainly study the log-behavior of \(\{U_n\}_{n\ge 3}\) and \(\{V_n\}_{n\ge 2}\). We prove that \(\{U_n\}_{n\ge 6}\) and \(\{V_n\}_{n\ge 6}\) are log-balanced. In addition, we discuss the log-behavior of some sequences involving \(U_n\) (\(V_n\)).



中文翻译:

Ménage 数字的对数行为

\(\{U_n\}_{n\ge 0}\)\(\{V_n\}_{n\ge 0}\)分别表示普通门数序列和直门数序列。在本文中,我们主要研究\(\{U_n\}_{n\ge 3}\)\(\{V_n\}_{n\ge 2}\) 的对数行为。我们证明\(\{U_n\}_{n\ge 6}\)\(\{V_n\}_{n\ge 6}\)是对数平衡的。此外,我们讨论了一些涉及\(U_n\) ( \(V_n\) ) 的序列的对数行为。

更新日期:2021-07-16
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