recurrence relation

递推关系

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A recurrence relation specifies each term of a sequence after a stated starting index in terms of earlier terms; an associated recursive specification also gives enough initial data to determine the sequence.

递推关系是在指定起始指标之后，用此前各项规定数列当前项的关系；递归定义还需给出足够的初始数据。

Example

$a_0=2$ and $a_n=3a_{n-1}+1$ for $n\ge1$ determine $2,7,22,67,\ldots$.

Usage and distinctions

The equation alone need not fix a sequence: a_n=2a_{n−1} has different solutions for different a_0. A recurrence need not be linear.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Joy Morris — Combinatorics, version 2.1.1Section 6.1, Definition 6.1.1 · Checked 2026-10-14

Translation sources

1. 上海交通大学 — CS0901 组合数学（2026）§2.3「用生成函数解递推」，开篇「递推关系」 · Checked 2026-10-14

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