1) fractional linear recursive sequence of number
分式线性递归数列
2) linear recursion sequence
线性递归数列
1.
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.
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)。
3) Fractional Recurrent Sequence
分式递归数列
1.
The Period of a Class of Fractional Recurrent Sequence;
一类分式递归数列的周期性
4) fractional linear recursive series
分式线性递推数列
1.
Application of matrix theory to solving the general formula of fractional linear recursive series;
矩阵理论在求分式线性递推数列通项公式中的应用
5) linear fraction recurrence
线性分式递推数列
6) homogeneous linear recurrent sequence of number
齐次线性递归数列
1.
This article provides the sufficient condition of how to judge if a sequence of number is a homogeneous linear recurrent sequence of number according to the formula of general term,and the structure of its recursive equation.
给出并证明了由数列的通项公式判定其是齐次线性递归数列的充分条件,以及其递归方程的构造。
补充资料：递归数列
| 递归数列 recursive sequence 一种用归纳方法给定的数列。例如，等比数列可以用归纳方法来定义，先定义第一项a1的值(a1≠0)，对于以后的项，用递推公式an+1＝qan（q≠0，n＝1，2，…）给出定义。一般地，递归数列的前k项a1，a2，…，ak为已知数，从第k＋1项起，由某一递推公式an+k＝f（an，an+1，…，an+k-1）( n＝1，2，…）所确定。k称为递归数列的阶数。例如 ，已知 a1＝1，a2＝1，其余各项由公式an+1＝an＋an-1（n＝2，3，…）给定的数列是二阶递归数列。这是斐波那契数列，各项依次为 1，1，2，3，5，8，13，21，…，同样，由递归式an+1－an ＝an－an-1( a1，a2为已知，n＝2，3，… ) 给定的数列，也是二阶递归数列，这是等差数列。 |
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