Recurring dreams with floor function?

f(n)=2n+3222n+12\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 [1,103)[1,10^3).
  • B. Eventually periodic with period in [103,106)[10^3,10^6).
  • C. Eventually periodic with period in [106,)[10^6,\infty).
  • D. Not eventually periodic.

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