Zeckendorf Representation

Each new term in the Fibonacci sequence is generated by adding the previous two terms.

Starting with $1$ and $2$, the first $10$ terms will be: $1$, $2$, $3$, $5$, $8$, $13$, $21$, $34$, $55$, $89$.

Every positive integer can be uniquely written as a sum of nonconsecutive terms of the Fibonacci sequence. For example, $100$ = $3$ + $8$ + $89$.

Such a sum is called the Zeckendorf representation of the number.

For any integer n>$0$, let z(n) be the number of terms in the Zeckendorf representation of n.

Thus, z($5$) = $1$, z($14$) = $2$, z($100$) = $3$ etc.

Also, for $0<n<10^6$, $\sum z(n) = 7894453$.

Find $\sum z(n)$ for $0<n<10^{17}$.