  We present four different constructions of pattern-avoiding inversion
sequences, and use them to obtain expressions for the enumeration sequences of
22 distinct open cases. This completes the enumeration of inversion sequences
avoiding one or two patterns of length 3. Some of our constructions are based
on generating trees. Others involve pattern-avoiding words, which we also count
using generating trees. Furthermore, we introduce a generalization of inversion
sequences, which we call shifted inversion sequences. It is sometimes easier to
construct pattern-avoiding inversion sequences by seeing them as a particular
case of shifted inversion sequences.
