# [MOSP 2001] Counting number of sets

Let $$a_n$$ denote the number of nonempty sets $$S$$ such that:

(i)$$S \subseteq \{1,2,...,n\}$$

(ii) All elements of $$S$$ have the same parity;

(iii) Each element $$k\in S$$ such that $$k\geq 2|S|$$.

What is the value of $$a_{37}$$?

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