# Problem 297: Zeckendorf Representation

![graphic](img297.gif)

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