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Search: id:A129775
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| A129775 |
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Number of maximally clustered permutations in S_n; the maximally clustered permutations are those that avoid 3421, 4312 and 4321. |
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+0
2
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| 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equals INVERT transform of A001700 prefaced with a "1": (1, 1, 3, 10, 35, 126, 462,...) [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 26 2008]
Row sums of A155083. [From Paul Barry (pbarry(AT)wit.ie), Jan 19 2009]
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REFERENCES
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Jozsef Losonczy, Maximally clustered elements and Schubert varieties, Preprint (2006), to appear in Annals of Combinatorics.
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LINKS
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H. Denoncourt and B. Jones, The enumeration of maximally clustered permutations.
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FORMULA
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G.f.: (2x^2) / (-1+4x-2x^2+sqrt(1-4x)).
G.f.: 1/(1-x-x/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-..... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Jan 19 2009]
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EXAMPLE
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a(5)=78 because there are 78 permutations of size 5 that avoid 3421, 4312 and 4321.
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CROSSREFS
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Cf. A108600.
A001700 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 26 2008]
Sequence in context: A144169 A124292 A129776 this_sequence A054515 A150190 A150191
Adjacent sequences: A129772 A129773 A129774 this_sequence A129776 A129777 A129778
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KEYWORD
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nonn
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AUTHOR
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Brant Jones (brant(AT)math.washington.edu), May 17 2007
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