Question 12
Every positive integer $n$ can be uniquely written as a sum of one or more non-consecutive Fibonacci numbers $F_2=1,F_3=2,F_4=3,F_5=5,\ldots$, excluding $F_0$ and $F_1$. For example, $30=1+8+21=F_2+F_6+F_8$. Let $a_n$ be the number of terms in the Fibonacci representation of $n$; for example, $a_{30}=3$. What is $a_1+a_2+\cdots+a_{54}$?