求数列a1=1,a2=2,a（n+2）=3a（n+1）+2an(n属于正整数)的通项公式

a(n+2)=3a(n+1)+2an
The aux.eqaution
x^2-3x-2 =0
x = (3+√17)/2 or (3-√17)/2
let
an = A[(3+√17)/2]^(n-1) + B[(3-√17)/2]^(n-1)
n=1
a1=A+B= 1 (1)
n=2
a2 = A(3+√17)/2 +B(3-√17)/2 = 2 (2)
[(3+√17)/2] (1) - (2)
√17B = (-1+√17)/2
B = (1/2)( 1 - √17/17)
[(3-√17)/2](1) - (2)
-√17A = -(1+√17)/2
A= (1/2)(1 +√17/17 )
an =(1/2)(1 +√17/17 )[(3+√17)/2]^(n-1) + (1/2)( 1 - √17/17)[(3-√17)/2]^(n-1)