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Find all possible finite sequences {n_0,n_1,...,n_k}

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October 5, 2010
combinatorics proposedcombinatorics

Problem Statement

Find all possible finite sequences {n0,n1,n2,,nk}\{n_0, n_1, n_2, \ldots, n_k \} of integers such that for each i,ii, i appears in the sequence nin_i times (0ik).(0 \leq i \leq k).