2018 UNCO Math Contest II Problems/Problem 9
Call a set of integers Grassilian if each of its elements is at least as large as the number of elements in the set. For example, the three-element set is not Grassilian, but the six-element set is Grassilian. Let be the number of Grassilian subsets of . (By definition, the empty set is a subset of every set and is Grassilian.) (a) Find , , and . (b) Find a recursion formula for . That is, find a formula that expresses in terms of (c) Give an explanation that shows that the formula you give is correct.
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