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Search: id:A129869
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| A129869 |
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Number of positive clusters of type D_n. |
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+0
1
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| -1, 1, 5, 20, 77, 294, 1122, 4290, 16445, 63206, 243542, 940576, 3640210, 14115100, 54826020, 213286590, 830905245, 3241119750, 12657425550, 49483369320, 193641552390, 758454277620
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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This is also the number of antichains in the poset of positive-but-not-simple roots of type Dn
If Y is a fixed 2-subset of a (2n+1)-set X then a(n+1) is the number of (n+2)-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Oct 28 2007
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REFERENCES
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S. Fomin and A. Zelevinsky, Y-systems and generalized associahedra, Ann. of Math. (2) 158 (2003), no. 3, 977-1018.
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LINKS
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Milan Janjic, Two Enumerative Functions
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FORMULA
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a(n)=(3*n-4)/n*binomial(2*n-3,n-1)
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EXAMPLE
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a(3)=5 because the type D3 is the same as type A3 and there are 5 positive clusters among the 14 clusters in type A3
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PROGRAM
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(3*n-4)/n*binomial(2*n-3, n-1) $n=1..22; (MuPAD code)
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CROSSREFS
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Cf. A051924.
Adjacent sequences: A129866 A129867 A129868 this_sequence A129870 A129871 A129872
Sequence in context: A000758 A005283 A057552 this_sequence A079737 A028814 A079820
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KEYWORD
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sign
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AUTHOR
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F. Chapoton (fchapoton(AT)voila.fr), May 24 2007
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