how to go about this recursion question any hints or references I should look into
To give you a starting point, rewrite your recursion equation as
$\displaystyle s_{n + 1} = 4 s_{n} + 4 s_{n - 1}$
$\displaystyle s_{n + 2} - 4 s_{n + 1} - 4 s_{n} = 0$
What is the characteristic equation look like?
Can you take it from here?
-Dan