Problem $1.(4+8=12$ points$)$ What does this code do$?$

You encounter the following mysterious piece of code.

Algorithm $1$: Mystery Function

Function F$($n$))$:

If n $=0$ :

Return $(2,1)$

Else

b $1$

For i from $1$ to n

b $2$b

$($u$,$ v$)$ F$($n $1)$

Return $($u $+$ b$,$ v $$ b$)$