Uniform random generations and rejection method(I) with binomial majorant

We present three simple algorithms to uniformly generate `Fibonacci words’ (i.e., some words that are enumerated by Fibonacci numbers), Schr{ö}der trees of size $n$ and Motzkin left factors of size $n$ and final height $h$. These algorithms have an average complexity of $O(n)$ in the unit-cost RAM model.