cp's OEIS Frontend

A137536 Number of permutations in S_n avoiding {bar 4}2153 (i.e., every occurrence of 2153 is contained in an occurrence of a 42153).

%I A137536 #21 Jul 10 2023 19:51:33
%S A137536 1,1,2,6,23,104,532,3002,18375,120559,840480,6184729,47788384,
%T A137536 386126534,3251434927,28454039404
%N A137536 Number of permutations in S_n avoiding {bar 4}2153 (i.e., every occurrence of 2153 is contained in an occurrence of a 42153).
%C A137536 From _Lara Pudwell_, Oct 23 2008: (Start)
%C A137536 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.
%C A137536 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 A137536 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 A137536 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 A137536 Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/papers/pudwell_thesis.pdf">Enumeration Schemes for Pattern-Avoiding Words and Permutations</a>, Ph. D. Dissertation, Math. Dept., Rutgers University, May 2008.
%H A137536 Lara Pudwell, <a href="https://doi.org/10.37236/301">Enumeration schemes for permutations avoiding barred patterns</a>, El. J. Combinat. 17 (1) (2010) R29.
%e A137536 See example in A137546.
%Y A137536 Cf. A137536-A137548, A117107.
%K A137536 nonn,more
%O A137536 0,3
%A A137536 _Lara Pudwell_, Apr 25 2008
%E A137536 a(8)-(15) from _Lars Blomberg_, Jun 04 2018
%E A137536 a(0)=1 prepended by _Alois P. Heinz_, Jul 10 2023