# Approximating rational generating functions

Suppose we have a initial segment $x_1,\ldots,x_N$ (for reasonably large $N$) of a sequence of natural numbers $(x_i)$. We have reason to believe the generating function $\sum_{i=0}^\infty x_iX^i$ is rational. Are there any methods one could use to guess/approximate this generating function as a quotient of polynomials $P(X)/Q(X)$ with small degrees (relative to $N$).

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