  We show that the number of members of S_n avoiding any one of five specific
triples of 4-letter patterns is given by sequence A111279 in OEIS, which is
known to count weak sorting permutations. By numerical evidence, there are no
other (non-trivial) triples of 4-letter patterns giving rise to this sequence.
We make use of a variety of methods in proving our result, including
recurrences, the kernel method, direct counting, and bijections.
