MathNet 2017-part-04 — 176 problems (EN–VI) Question 110

Define a sequence of integers as follows: $a_{1}=1$, $a_{2}=2$, and for $k \in \mathbb{N}$, $a_{k+2}=a_{k+1}+a_{k}$. How many different ways are there to write $2017$ as a sum of distinct elements of this sequence?