The sequence $a_1,a_2…$ , is defined by the equations $a_1=1$ and $a_n=n.a_{[n/2]}$ for $n>1$. Prove that $a_n>n^2$ for $n>11$.
Problem
Source: VIII International Festival of Young Mathematicians Sozopol 2017, Theme for 10-12 grade
Tags: algebra, Sequence