%I
%S 1,1,3,12,57,304,1765,10943,71519,488186,3456526,25251479,189545179
%N Number of permutations in S_n avoiding 21{bar 3}54 (i.e., every occurrence of 2154 is contained in an occurrence of a 21354) and such that the graph corresponding to the permutation is connected (see "Forestlike permutations" below).
%C From _Lara Pudwell_, Oct 23 2008: (Start)
%C A permutation p avoids a pattern q if it has no subsequence that is orderisomorphic to q. For example, p avoids the pattern 132 if it has no subsequence abc with a < c < b.
%C Barred pattern avoidance considers permutations that avoid a pattern except in a special case. Given a barred pattern q, we may form two patterns, q1 = the sequence of unbarred letters of q and q2 = the sequence of all letters of q.
%C A permutation p avoids barred pattern q if every instance of q1 in p is embedded in a copy of q2 in p. In other words, p avoids q1, except in the special case that a copy of q1 is a subsequence of a copy of q2.
%C For example, if q = 5{bar 1}32{bar 4}, then q1 = 532 and q2 = 51324. p avoids q if every for decreasing subsequence acd of length 3 in p, one can find letters b and e so that the subsequence abcde of p has b < d < c < e < a. (End)
%H M. BousquetMÃ©lou and S. Butler, <a href="http://arXiv.org/abs/math.CO/0603617">Forestlike permutations</a>, arXiv:math/0603617 [math.CO], 2006.
%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/papers/pudwell_thesis.pdf">Enumeration Schemes for PatternAvoiding Words and Permutations</a>, Ph. D. Dissertation, Math. Dept., Rutgers University, May 2008.
%e See example in A137546.
%Y Cf. A137536, A137537, A137538, A137539, A137540, A137541, A137542, A137543, A137544, A137545, A137546, A137547, A137548.
%K nonn,more
%O 1,3
%A _Steve Butler_, Apr 18 2006
