Functions can be a problem

Algebra Level 5

Let \(Z_{\ge 0}\) denotes the set of all nonnegative integers. Determine the number of functions \(f:Z_{\ge 0}\rightarrow Z_{\ge 0}\) that satisfy the relation

\[\large{f(f(f(n)))=f(n+1)+1}\]

for all \(n\in Z_{\ge 0}\)

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