Given the recurrence an=an−1+an−2a_n = a_{n-1} + a_{n-2}an=an−1+an−2 with a0=0,a1=1a_0=0, a_1=1a0=0,a1=1, what is the generating function A(x)A(x)A(x)?
x1−x−x2\frac{x}{1-x-x^2}1−x−x2x
11−x−x2\frac{1}{1-x-x^2}1−x−x21
x1+x+x2\frac{x}{1+x+x^2}1+x+x2x
x1−x+x2\frac{x}{1-x+x^2}1−x+x2x