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The Collatz map is defined for a positive even integer as half that integer,and for a positive odd integer as that integer threefold, plus one. The Collatzconjecture states that when the map is iterated the number one is eventuallyreached. We study permutations that arise as sequences from this iteration. Weshow that permutations of this type of length up to 14 are enumerated by theFibonacci numbers. Beyond that excess permutations appear. We will explain theappearance of these excess permutations and give an upper bound on the exactenumeration.

Collatz meets Fibonacci