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Weights sets

Source: St Petersburg Olympiad 2015, Grade 11, P3

October 17, 2017
combinatoricsnumber theory

Problem Statement

There are weights with mass 1,3,5,....,2i+1,...1,3,5,....,2i+1,... Let A(n)A(n) -is number of different sets with total mass equal nn( For example A(9)=2A(9)=2, because we have two sets 9=9=1+3+59=9=1+3+5). Prove that A(n)≤A(n+1)A(n) \leq A(n+1) for n>1n>1
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