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Find the n-th term of the sequence

Source: Vietnam NMO 1986 Problem 6

February 6, 2009
combinatorics unsolvedcombinatorics

Problem Statement

A sequence of positive integers is constructed as follows: the first term is 1 1, the following two terms are 2 2, 4 4, the following three terms are 5 5, 7 7, 9 9, the following four terms are 10 10, 12 12, 14 14, 16 16, etc. Find the n n-th term of the sequence.
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