principal classes classes avoiding two patterns of length 4 classes avoiding only length 3 patterns subclasses of Av(123) classes equinumerous to Av(132, 231) classes counted by the Schröder numbers classes whose enumeration starts 1, 2, 6, 20 classes whose systems of equations we cannot solve 6 out of the 7 symmetry classes avoiding 1 pattern of length 4 the four classes avoiding 2 or 3 patterns length 4 that are conjectured to be non-D-finite