https://www.docin.com/p-1191736306.html
https://wenku.baidu.com/view/07029255bcd126fff6050b01.html
例1 ，$$a_1 = 0,a_2=1,a_3=3,a_{n+3}=2a_{n+2}+a_{n+1}-2a_{n}$$
$$ x^3=2x^2+x-2,x_1=1,x_2=-1,x_3=2 $$
$$ a_n=A_1b_{1n}+A_2b_{2n}+A_3b_{3n} $$
$$b_{1n} = x_1^{n-1}=1,b_{2n} = x_2^{n-1}=(-1)^{n-1},b_{3n} = x_3^{n-1}=2^{n-1}$$
$$\left\{\begin{matrix} A_1+A_2+A_3=0 \\ A_1-A_2+2A_3=1\\ A_1+A_2+4A_3=3 \end{matrix}\right.$$
$$A_1=-1,A_2=0,A_3=1 $$
$$ a_n=A_1b_{1n}+A_2b_{2n}+A_3b_{3n} = 2^{n-1}-1$$