倒数递推数列

The Reciprocal Recurrence Sequence

本文给出了倒数递推数列的定义，求出了它的通项公式，并指出它与二阶线性差分数列的内在联系。

Since Fibonacci sequence was borne, the Linear Recurrence Sequence (LRS) {an}:an+2=pan+1 + qan (1)has become increasingly popular. Accordingly, the articles on it defy enumeration. However, almost none of them concerns the Reciprocal Recurrence Sequence (RRS). In this paper, we propose the definition of the RRS, give the formula of its general term, and show the intrinsic relations between the LRS and the RRS.