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Search: id:A006659
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| A006659 |
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Closed meander systems of order n+1 with n components.
(Formerly M2025)
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+0
3
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| 2, 12, 56, 240, 990, 4004, 16016, 63648, 251940, 994840, 3922512, 15452320, 60843510, 239519700, 942871200, 3711935040, 14615744220, 57562286760, 226760523600, 893550621600, 3522078700140, 13887053160552
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n)=total number of long interior inclines in all Dyck (n+2)-paths. An incline is a maximal subpath of like steps (all Us or all Ds); interior means it does not start or end the path; long means of length >=2. Example: for n=1, the 5 Dyck 3-paths are shown with long interior inclines in uppercase: uuuddd, uududd, udUUdd, ududud, uuDDud, and so a(1)=2. - David Callan (callan(AT)stat.wisc.edu), Jul 03 2006
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REFERENCES
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S. K. Lando and A. K. Zvonkin "Plane and projective meanders", Theoretical Computer Science Vol. 117 (1993) p. 232.
S. K. Lando and A. K. Zvonkin "Plane and projective meanders", S\'{e}ries Formelles et Combinatoire Alg\'{e}brique. Laboratoire Bordelais de Recherche Informatique, Universit\'{e} Bordeaux I, 1991, pp. 287-303.
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LINKS
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P. Di Francesco, O. Golinelli and E. Guitter, Meander, folding and arch statistics.
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FORMULA
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G.f.: 32/{sqrt(1-4x)(1+sqrt(1-4x))^4}.
a(n) = (n+1) * A002057(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 31 2003
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CROSSREFS
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Cf. A005315, A005316.
Equals 2*A002694(n+1).
A diagonal of triangle A008828.
Sequence in context: A124723 A122229 A127216 this_sequence A127221 A020522 A037130
Adjacent sequences: A006656 A006657 A006658 this_sequence A006660 A006661 A006662
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KEYWORD
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nonn,easy,nice
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AUTHOR
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D. Ivanov, S. K. Lando and A. K. Zvonkin (zvonkin(AT)labri.u-bordeaux.fr)
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