How to find its closed-form? here is a sequence defined by the below recursion formula:
$$a_n=2a_{n-1}+a_{n-2}$$
where $n \in \mathbb{N}$ and $a_0=1,a_1=2$.how to find its closed-form.

If we write $E^ra_n=a_{n+r},$
the characteristic/auxiliary equation becomes $E^2-2E-1=0,E=1\pm\sqrt2$
So, the  complementary function $a_n=A(1+\sqrt2)^n+B(1-\sqrt2)^n$ where $A,B$ are indeterminate constants to be determined from the initial condition.
$a_0=A+B,$ But $a_0=1$ So, $A+B=1$
and $a_1=A(1+\sqrt2)+B(1-\sqrt2)=2$  
Now, solve for $A,B$
