Number of partitions of integer into parts repeated <= 2 times

The generating function for the number of such partitions is $$G(q) = \prod_{i=0}^{\infty}(1+q^i+q^{2i})$$ - that much I understand. Is there any way to transform it into a form $\sum_{n=0}^{\infty}p(n)q^n$, so that $p(n)$ becomes available?

Thank you.

I wouldn't expect a closed-form formula for $p(n)$. The function is tabulated at http://oeis.org/A000726 which also has information and links (but no closed-form formula).