| 关于杨辉三角错位变体和克隆变体的猜想 |
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| 引用本文： | 邹峰,郭小丽.关于杨辉三角错位变体和克隆变体的猜想[J].武汉职业技术学院学报,2006,5(1):114-117. |
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| 作者姓名： | 邹峰 郭小丽 |
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| 作者单位： | 武汉职业技术学院,商学院,湖北,武汉,430074 |
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| 摘 要： | 从杨辉三角的两种基本变体即错位变体和克隆变体的概念,提出两个猜想,并证明两种变体的各行和与形如a_(n k l)=a_(n k) a_n的线性递归数列的对应关系,同时给出这类递归数列的两种通项公式1)。借助杨辉三角及其变体研究线性递归数列的性质将会是一种新颖而且有效的方法。
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| 关 键 词： | 杨辉三角 线性递归数列 通项公式 二项式系数 斐波那契数列 |
| 文章编号： | 1671-931X（2006）01-0114-04 |
| 收稿时间： | 2005-10-27 |
| 修稿时间： | 2005年10月27 |
On Conjectures of Two Deformations of Pascal's Triangle |
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| ZOU Feng,GUO Xiao-li.On Conjectures of Two Deformations of Pascal''''s Triangle[J].Journal of Wuhan Institute of Technology,2006,5(1):114-117. |
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| Authors: | ZOU Feng GUO Xiao-li |
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| Institution: | Commercial College, Wuhan Institute of Technology, Wuhan 430074, China |
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| Abstract: | This paper presents the concepts about two basic deformations of Pascal's triangle, that is, Shifted Deformation and Clone Deformation. Then, two conjectures are brought forward, which are proved that there are relations between the two deformations and a class of linear recursion sequences such as a_(n k l)=a_(n k) a_n. It also introduces two kinds of general term formulas of these number sequences:l)This paper suggests that it should be a novel and efficient method to study linear recursion sequences using Pascal's triangle and its deformations. |
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| Keywords: | Pascal's triangle linear recursion sequence general term formula binomial coefficient Fibonacci sequence |
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