Ascent sequences avoiding a triple of 3-letter patterns and Fibonacci numbers

We consider triples τ of 3-letter patterns for which ascent sequences that avoid τ are counted by Fibonacci-related numbers. Several cases are equivalent to avoiding a pair of 3-letter patterns and have already been treated using generating functions. Here we give direct proofs of all our results. We also consider avoiders for some quadruples of 3-letter patterns.

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