Prove using induction, that sequence is correct for all positive integers:

$\displaystyle a_{1}=1$

$\displaystyle a_{2}=4$

$\displaystyle a_{3}=12$

$\displaystyle a_{n}=4a_{n-1}-4a_{n-2}$

I would like you to show me the whole proof, I am learning now the elementary maths and I do not know how to prove it exactly by induction...

Sorry for my english...

Can anybody help me, please?