Integer part of $(1 + \sqrt{2})^n$

Give an algorithm to compute the integer part of

$$(1+ \sqrt{2})^n$$

in number of operations which is polynomial in $\log n$.

Note: I had a mistake earlier by using time, instead of number of operations. Even though we use only polynomial in $\log n$ integer operations, the running time will be $\Omega(n)$, as we are dealing with $\theta(n)$ bit integers.

[Solution]