The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A117107 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 "Forest-like permutations" below). 2
 1, 1, 3, 12, 57, 304, 1765, 10943, 71519, 488186, 3456526, 25251479, 189545179 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS From Lara Pudwell, Oct 23 2008: (Start) A permutation p avoids a pattern q if it has no subsequence that is order-isomorphic to q. For example, p avoids the pattern 132 if it has no subsequence abc with a < c < b. 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. 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. 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) LINKS M. Bousquet-Mélou and S. Butler, Forest-like permutations, arXiv:math/0603617 [math.CO], 2006. Lara Pudwell, Enumeration Schemes for Pattern-Avoiding Words and Permutations, Ph. D. Dissertation, Math. Dept., Rutgers University, May 2008. EXAMPLE See example in A137546. CROSSREFS Cf. A137536, A137537, A137538, A137539, A137540, A137541, A137542, A137543, A137544, A137545, A137546, A137547, A137548. Sequence in context: A103370 A094149 A291695 * A159609 A128326 A323631 Adjacent sequences:  A117104 A117105 A117106 * A117108 A117109 A117110 KEYWORD nonn,more AUTHOR Steve Butler, Apr 18 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 6 18:51 EDT 2020. Contains 333286 sequences. (Running on oeis4.)