query on finding numeric function of a generating function For the given generating function $A(z)=1/(1-x^3)$ what will be the numeric function..
I can find out for $A(z)=1/(1-x^2)$ but in the first case we get two factor in the denominator $(1-x)$ and $(x^2+x+1)$, now how do we find the numeric function for $1/(x^2+x+1)$?

We don't need to factorize the denominator. Let's recall the geometric series expansion.
\begin{align*}
\frac{1}{1-y}=1+y+y^2+y^3+\cdots\qquad\qquad  |y|<1
\end{align*}

We obtain with $y=x^3$
  \begin{align*}
\frac{1}{1-x^3}=1+x^3+x^6+\cdots\qquad\qquad |x|<1
\end{align*}
  and  the coefficients are $1$ if the powers of $x$ are  congruent $0\,\textrm{mod}(3)$ and $0$ otherwise.

