Recurring dreams with floor function?

$\Large f(n)= \left \lfloor 2^{n+\frac{3}{2}} \right \rfloor - 2 \left \lfloor 2^{n+\frac{1}{2}} \right \rfloor$

The above function is defined on the natural numbers. Which of the following describes the periodicity of the function?

• A. Eventually periodic with period in $[1,10^3)$.
• B. Eventually periodic with period in $[10^3,10^6)$.
• C. Eventually periodic with period in $[10^6,\infty)$.
• D. Not eventually periodic.

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