Help with mathematical induction

I have a series: $\displaystyle a_{0},a_{1},a_{2}...$

$\displaystyle a_{0}=1$

$\displaystyle a_{n+1}=\frac{((a_{n})^{2}+9)}{6}\hspace{6} n\geq 1$

i want to find a explicit form for $\displaystyle a_{n}$

and prove it with induction.

i calculated some values to use:

$\displaystyle a_{1}=\frac{5}{3}$

$\displaystyle a_{2}=\frac{53}{27}

$

i tried something like this:

$\displaystyle a_{n}=\frac{3n^4+n^2+1}{?}$

but im having a hard time finding a dominator that works with my values.

Maybe i´m doing it all wrong :)

regards mechaniac