A(n+2)-2An=0
A(n+2)=2An
A(n+2)/An=2
{An/A(n-2)}等比数列公比2,首项为A1=1 A2=2
An=2^(n-1) /2 (n为奇数)
An=2*2^(n-2)/2= 2^n/2 (n为偶数)
sn=[2^(n+1)/2 -1]/(2-1)+[2^(n+1)/2 -2]/(2-1)
=2^(n+3)/2 -3 (n为奇数)
sn=[2^n/2 -1]/(2-1)+[2*2^n/2 -2]/(2-1)
=3*2^n/2 -3 (n为偶数)