CeilingAndFloor LinearRecursion PUMaC Difficult
2014

Problem - 2487
There is a sequence with $a(2) = 0$, $a(3) = 1$ and $a(n) = a(\lfloor{\frac{n}{2}}\rfloor)+a(\lceil{\frac{n}{2}}ceil)$ for $n\ge 4$. Find $a(2014)$.