RU-SPB 2015 Problem 113

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