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A047970
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Sums along antidiagonals of A047969.
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18
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1, 2, 5, 14, 43, 144, 523, 2048, 8597, 38486, 182905, 919146, 4866871, 27068420, 157693007, 959873708, 6091057009, 40213034874, 275699950381, 1959625294310, 14418124498211, 109655727901592, 860946822538675, 6969830450679864
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Comment from Lara Pudwell (Lara.Pudwell(AT)valpo.edu), 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)
Number of ordered factorizations over the Gaussian polynomials.
Apparently, also the number of permutations in S_n avoiding {bar 3}{bar 1}542 (i.e. every occurrence of 542 is contained in an occurrence of a 31542). - Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Apr 25 2008
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REFERENCES
| See Andrews, Partitions, (1976) page 242 for table of Gaussian polynomials.
C. Callan, The number of bar(31)542-avoiding permutations, arXiv:1111.3088
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LINKS
| Lara Pudwell, Enumeration Schemes for Pattern-Avoiding Words and Permutations, Ph. D. Dissertation, Math. Dept., Rutgers University, May 2008.
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EXAMPLE
| a(3)=1+5+7+1=14.
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CROSSREFS
| Partial sums are in A026898, A003101.
Sequence in context: A014327 A173437 A137550 * A137551 A160701 A148333
Adjacent sequences: A047967 A047968 A047969 * A047971 A047972 A047973
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KEYWORD
| nonn
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com)
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