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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
a(n)=number of corners in all parallelogram polyominoes of semiperimeter n+3. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 09 2008]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
M. P. Delest, D. Gouyou-Beauchamps and B. Vauquelin, Enumeration of parallelogram polyominoes with given bond and site parameter, Graphs and Combinatorics, 3(1987),325-339. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 09 2008]
M. Delest, J. P. Dubernard and I. Dutour, Parallelogram polyominoes and corners, J. Symbolic Computation, 20(1995),503-515. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 09 2008]
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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
a(n)=2*binom(2n+2,n-1). [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 09 2008]
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MAPLE
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seq(2*binomial(2*n+2, n-1), n=1..22); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 09 2008]
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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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