\[ \large 2^A = \sum_{n=0}^{2016} \left[ (-1)^{n(n-1)/2} \times 3^{\lfloor n/2 \rfloor } \times \dbinom {2016} n\right ] \]

What is the value of \(A\)?

**Notations**:

\( \lfloor \cdot \rfloor \) denotes the floor function.

\( \dbinom MN \) denotes the binomial coefficient, \( \dbinom MN = \dfrac{M!}{N!(M-N)!} \).

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