Obtaining recurrence relation from polynomial

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Consider

$P(n)=(\frac{1}{3})^n$ for $n\in\mathbb{Z}$

From this, we can obtain the recurrence relation

$P(n)=\frac{10}{3}\cdot P(n-1)-P(n-2)$ for $n\geq2$

How would we go about obtaining this relation from $P(n)$ given above?