| 一类递推数列的周期性 |
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| 引用本文： | 乐茂华. 一类递推数列的周期性[J]. 大学数学, 2007, 23(4): 160-162 |
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| 作者姓名： | 乐茂华 |
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| 作者单位： | 湛江师范学院,数学系,广东,湛江,524048 |
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| 基金项目： | 国家自然科学基金项目(10271104)，广东省自然科学基金项目(06029035) |
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| 摘 要： | 设k,m是适合k>2的正整数,p=2cos(2π)/k.本文证明了:如果数列A={an}n=0∞满足递推关系an+2m=pan+m-an(n≥0),则A是周期数列,它的最小正周期是km的约数.另外,给出了最小正周期小于km的非零数列的例子.
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| 关 键 词： | 递推数列 周期性 最小正周期 |
| 文章编号： | 1672-1454（2007）04-0160-03 |
| 修稿时间： | 2005-10-30 |
The Periodicity for a Class of Recurring Sequences |
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| LE Mao-hua. The Periodicity for a Class of Recurring Sequences[J]. College Mathematics, 2007, 23(4): 160-162 |
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| Authors: | LE Mao-hua |
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| Affiliation: | Department of Mathematics, Zhanjiang Normal College, Zhanjiang, Guangdong 524048, China |
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| Abstract: | Let k,m be positive integer with k>2,and let p=2cos(2π)/k.In this paper we prove that if the sequence A={an}∞n=0 satisfy the recurrence relation an+2m=pan+m-an(n≥0),then A is a periodic sequence and its least positive period is a divisor of km.Moreover,some sequences which periods less than km,are given. |
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| Keywords: | recurring sequence periodicity least positive period |
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