Which one of the following best expresses the generating function sequence $\{a_n\}$, for the given closed form representation?
$$F(x) = \frac{1}{1-x-x^2}$$
- $a_n=a_{n-1}+3, n>0, a_0=1$
- $a_n=a_{n-1}+a_{n-2}, n>1, a_0=1, a_1=1$
- $a_n=2n+3, n>1$
- $a_n=2a_{n-1}+3, n>1, a_0=1$