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A129775 Number of maximally clustered permutations in S_n; the maximally clustered permutations are those that avoid 3421, 4312 and 4321. +0
2
1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750 (list; graph; listen)
OFFSET

1,2

COMMENT

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]

REFERENCES

Jozsef Losonczy, Maximally clustered elements and Schubert varieties, Preprint (2006), to appear in Annals of Combinatorics.

LINKS

H. Denoncourt and B. Jones, The enumeration of maximally clustered permutations.

FORMULA

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]

EXAMPLE

a(5)=78 because there are 78 permutations of size 5 that avoid 3421, 4312 and 4321.

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Brant Jones (brant(AT)math.washington.edu), May 17 2007

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.


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