Counting the Number of Elements of a Set.

Define sets \(A_i =\{i, i+1\}\) and \(B_i=\{A_1, A_2,.....,A_i\}.\)

\(F_i\) is the set of all possible sets that can be formed by taking union of one or more elements of \(B_i\). For example, \(F_2 =\{A_1, A_2, A_1\cup A_2\}.\)

Find the number of distinct elements of \(F_{15}\).

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