MathDB
Non-decreasing integ seq. with sum of terms is equal to n

Source: Turkey TST 2003 - P6

April 6, 2013
combinatorics proposedcombinatorics

Problem Statement

For all positive integers nn, let p(n)p(n) be the number of non-decreasing sequences of positive integers such that for each sequence, the sum of all terms of the sequence is equal to nn. Prove that 1+p(1)+p(2)+⋯+p(n−1)p(n)≤2n.\dfrac{1+p(1)+p(2) + \dots + p(n-1)}{p(n)} \leq \sqrt {2n}.
Back to ProblemsView on AoPS