A(n+2)-3A(n+1)+2An=0A1=1,A2=3则特征方程是x^2-3x+2=0x1=1,x2=2所以An==C1*x1^n+C2*x2^n=C1*1^n+C2*2^n=C1+C2*2^n把A1=1,A2=3代入A1=1=C1+2C2A2=3=C1+4C2C2=1,C1=-1An=-1+2^n