设f(x)=a(x+2)^2-1;由f(0)=3得：a=1;所以f(x)=x^2+4x+3=(x+2)^2-1
所以f(an)=9n^2-1=(an+2)^2-1得：an+2=3n,或an+2=-3n
即an=3n-2,或an=-3n-2
所以数列{an}一定是等差数列