# An elementary sequence question [closed]

Define an infinite sequence, $a(n)$, such that, $a(1)=a(2)=1$; $$a(n)=a(a(n-1))+a(n-a(n-1)),\forall n\geq 3.$$ Show that, for every $n\geq 1$, $a(2n)\leq 2a(n)$.
• It is obviously well defined because $a(n+1)$ is either equal to $a(n)$ or to $a(n)+1$ for every $n$, so $a(n)< n$ for $n\ge 2$. But this site is not for olympiad problems. – Mark Sapir Jan 14 '18 at 4:05