Search: id:A005315
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%I A005315 M1862
%S A005315 1,1,2,8,42,262,1828,13820,110954,933458,8152860,73424650,678390116,
%T A005315 6405031050,61606881612,602188541928,5969806669034,59923200729046,
%U A005315 608188709574124,6234277838531806,64477712119584604,672265814872772972,
               7060941974458061392
%N A005315 Closed meandric numbers (or meanders): ways a loop can cross a road 2n 
               times.
%C A005315 There is a 1-1-correspondence between loops crossing a road 2n times 
               and lines crossing a road 2n-1 times.
%D A005315 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005315 For additional references see A005316.
%D A005315 V. I. Arnol'd, A branched covering of CP^2->S^4, hyperbolicity and projective 
               topology [ Russian ], Sibir. Mat. Zhurn., 29 (No. 2, 1988), 36-47 
               = Siberian Math. J., 29 (1988), 717-725.
%D A005315 B. Bobier and J. Sawada, A fast algorithm to generate open meandric systems 
               and meanders, preprint, 2007.
%D A005315 Franz, Reinhard O. W. and Earnshaw, Berton A. A constructive enumeration 
               of meanders. Ann. Comb. 6 (2002), no. 1, 7-17.
%D A005315 I. Jensen, A transfer matrix approach to the enumeration of plane meanders. 
               J. Phys. A 33, 5953-5963 (2000).
%D A005315 I. Jensen and A. J. Guttmann, Critical exponents of plane meanders. J. 
               Phys. A 33, L187-L192 (2000).
%D A005315 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.
%D A005315 S. K. Lando and A. K. Zvonkin, Meanders, Selecta Mathematica Sovietica, 
               Vol. 11, Number 2, pp. 117-144, 1992.
%D A005315 S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Theoretical 
               Computer Science Vol. 117, p227-241, 1993.
%D A005315 A. Phillips, Simple Alternating Transit Mazes, preprint. Abridged version 
               appeared as ``La topologia dei labirinti,'' in M. Emmer, editor, 
               L'Occhio di Horus: Itinerari nell'Imaginario Matematico. Istituto 
               della Enciclopedia Italia, Rome, 1989, pp. 57-67.
%D A005315 V. R. Pratt, personal communication.
%D A005315 J. A. Reeds and L. A. Shepp, An upper bound on the meander constant, 
               preprint, May 25, 1999. [Obtains upper bound of 13.01]
%D A005315 M. A. Sainte-Lagu\"{e}, Les R\'{e}seaux (ou Graphes)}, M\'{e}morial des 
               Sciences Math\'{e}matiques, Fasc. 18, Gauthier-Villars, Paris, 1926, 
               p. 47.
%H A005315 I. Jensen, <a href="b005315.txt">Table of n, a(n) for n = 0..24</a> [from 
               link below]
%H A005315 R. Bacher, <a href="http://www-fourier.ujf-grenoble.fr/cgi-bin/qau_prep.pl?AutorName=BACHER">
               Meander algebras</a>
%H A005315 P. Di Francesco, O. Golinelli and E. Guitter, <a href="http://arXiv.org/
               abs/hep-th/9506030">Meander, folding and arch statistics.</a>
%H A005315 Erich Friedman, <a href="a005315.gif">Illustration of initial terms</
               a>
%H A005315 I. Jensen, <a href="http://www.ms.unimelb.edu.au/~iwan/">Home page</a>
%H A005315 I. Jensen, <a href="http://www.ms.unimelb.edu.au/~iwan/meanders/series/
               closed.meanders.ser">More terms</a>
%H A005315 I. Jensen, <a href="http://arXiv.org/cond-mat/9910313">Enumeration of 
               plane meanders</a>
%H A005315 A. Panayotopoulos and P. Tsikouras, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">Meanders and Motzkin Words</a>, J. Integer 
               Seqs., Vol. 7, 2004.
%H A005315 A. Phillips, <a href="http://www.math.sunysb.edu/~tony/mazes/index.html">
               Mazes</a>
%H A005315 A. Phillips, <a href="http://www.math.sunysb.edu/~tony/mazes/satmaze.html">
               Simple, Alternating, Transit Mazes</a>
%H A005315 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/doc/sg.txt">
               My favorite integer sequences</a>, in Sequences and their Applications 
               (Proceedings of SETA '98).
%H A005315 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/
               Publications/books.html">Analytic Combinatorics</a>, 2009; see page 
               525
%Y A005315 These are the odd-numbered terms of A005316. Cf. A077054. For nonisomorphic 
               solutions see A077460.
%Y A005315 A column of triangle A008828.
%Y A005315 Sequence in context: A013999 A130649 A054993 this_sequence A121635 A002874 
               A078592
%Y A005315 Adjacent sequences: A005312 A005313 A005314 this_sequence A005316 A005317 
               A005318
%K A005315 nonn,nice
%O A005315 0,3
%A A005315 N. J. A. Sloane (njas(AT)research.att.com), J. A. Reeds (reeds(AT)idaccr.org)
%E A005315 Computed to n = 24 by Iwan Jensen.

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