Finding the recurrent formula

Question

I'm trying to solve the following problem:

Find the recurrent formula for: $a_{n+2}+4a_{n+1}+4a_n=0; a_0=1, a_1=3.$

I would probably want to calculate the first few elements in the sequence, however I fail right at the start. How can I calculate elements when there are $a_{n+2}, a_{n+1}$ and $a_n$ and I only have two numbers $a_0$ and $a_1$ defined?

Thanks for any help

Answer 1

Since the characteristic roots are $-2,-2$ consider a linear combination of $(-2)^n$ and $n(-2)^n$