Guess The Golden Function

Algebra Level 5

$\large h(h(n))+h(n+1)=n+2$

Consider all functions $h:\mathbb N \to \mathbb N$ satisfying the functional equation above for all natural numbers $n$ .

Find the value of $h(2014)$ .

Hint: Try to find some initial values and then somehow try to bring the Golden Ratio into use. Golden Ratio is $\frac{1+\sqrt{5}}{2}$ .