Call a subset S \subseteq\{0,1, \ldots, 14\} sparse if x+1(\bmod 15) is not in S whenever x \in S. Find the number of sparse subsets such that the sum of their elements is a multiple of 15.
Call a subset S \subseteq\{0,1, \ldots, 14\} sparse if x+1(\bmod 15) is not in S whenever x \in S. Find the number of sparse subsets such that the sum of their elements is a multiple of 15.