I have a general question about recursion. When you're either evaluating a recursive definition like:

$\displaystyle f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n-3)$ for $\displaystyle n\geq3$

and trying to find a general formula for $\displaystyle f(n)$

or trying to give a recursive definition for a formula like:

$\displaystyle a_n = n(n+1)$

Is there an easier way to do it then look at the sequence and try to find some pattern between the 2 formulas, because I'm really bad at figuring about patters in sequences and forming formulas from them.

Any help would be greatly appreciated. Thank you.