  We classify all bi-vincular patterns of length two and three according to the
number of permutations avoiding them. These patterns were recently defined by
Bousquet-Melou et. al., and are natural generalizations of Babson and
Steingrimsson's generalized patterns.
  The patterns are divided into seven and 24 Wilf classes, for lengths two and
three, respectively. For most of the patterns an explicit form for the number
of permutations avoiding the pattern is given.
