# Combinatorics?

Let $S = \displaystyle\sum_{r=1}^{33}\left(r-\dfrac{2}{3} \right)\dbinom{97}{3r-2}$

Where $$S = k(2^{94}+\frac{1}{2})$$. Find $$\lfloor k \rfloor$$.

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

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