Guess The Golden Function

Algebra Level 5

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

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

Find the value of h(2014)h(2014).

Hint: Try to find some initial values and then somehow try to bring the Golden Ratio into use. Golden Ratio is 1+52\frac{1+\sqrt{5}}{2}.


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