Unverified Commit 1aaf8c86 authored by Lao K's avatar Lao K Committed by GitHub
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Update linear-recurrence.md

F的定义式采用更加严谨的写法
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### 做法

定义 $F(A(x))=\sum_{i=0}^nA_if_i$ ,那么答案就是 $F(x^n)$ 。
定义 $F(\sum c_ix^i)=\sum c_if_i$ ,那么答案就是 $F(x^n)$ 。

由于 $f_n=\sum_{i=1}^{k}f_{n-i}a_i$ ,对于 $F(x^n)=F(\sum_{i=1}^{k}a_ix^{n-i})$ ,所以 $F(x^n-\sum_{i=1}^k a_ix^{n-i})=F(x^{n-k}(x^k-\sum_{i=0}^{k-1}a_{k-i}x^i))=0$ 。