%I A005316 M0874
%S A005316 1,1,1,2,3,8,14,42,81,262,538,1828,3926,13820,30694,110954,252939,933458,
               2172830,8152860,19304190,73424650,
%T A005316 176343390,678390116,1649008456,6405031050,15730575554,61606881612,152663683494,
               602188541928,1503962954930,
%U A005316 5969806669034,15012865733351,59923200729046,151622652413194,608188709574124,
               1547365078534578,6234277838531806,15939972379349178,64477712119584604,
               165597452660771610,672265814872772972,1733609081727968492,7060941974458061392
%N A005316 Meandric numbers: number of ways a river can cross a road n times.
%C A005316 Number of ways that a river (or directed line) that starts in the South-West 
               and flows East can cross an East-West road n times (see the illustration).
%C A005316 Or, number of ways that an undirected line can cross a road with at least 
               one end below the road.
%D A005316 Alon, Noga and Maass, Wolfgang, Meanders and their applications in lower 
               bounds arguments. Twenty-Seventh Annual IEEE Symposium on the Foundations 
               of Computer Science (Toronto, ON, 1986). J. Comput. System Sci. 37 
               (1988), no. 2, 118-129.
%D A005316 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 A005316 V. I. Arnol'd, ed., Arnold's Problems, Springer, 2005; Problem 1989-18.
%D A005316 B. Bobier and J. Sawada, A fast algorithm to generate open meandric systems 
               and meanders, preprint, 2007.
%D A005316 Di Francesco, P. The meander determinant and its generalizations. Calogero-Moser-Sutherland 
               models (Montreal, QC, 1997), 127-144, CRM Ser. Math. Phys., Springer, 
               New York, 2000.
%D A005316 Di Francesco, P., SU(N) meander determinants. J. Math. Phys. 38 (1997), 
               no. 11, 5905-5943.
%D A005316 Di Francesco, P. Truncated meanders. Recent developments in quantum affine 
               algebras and related topics (Raleigh, NC, 1998), 135-162, Contemp. 
               Math., 248, Amer. Math. Soc., Providence, RI, 1999.
%D A005316 Di Francesco, P. Meander determinants. Comm. Math. Phys. 191 (1998), 
               no. 3, 543-583.
%D A005316 Di Francesco, P. Exact asymptotics of meander numbers. Formal power series 
               and algebraic combinatorics (Moscow, 2000), 3-14, Springer, Berlin, 
               2000.
%D A005316 Di Francesco, P., Golinelli, O. and Guitter, E., Meanders. In The Mathematical 
               Beauty of Physics (Saclay, 1996), pp. 12-50, Adv. Ser. Math. Phys., 
               24, World Sci. Publishing, River Edge, NJ, 1997.
%D A005316 Di Francesco, P., Golinelli, O. and Guitter, E. Meanders and the Temperley-Lieb 
               algebra. Comm. Math. Phys. 186 (1997), no. 1, 1-59.
%D A005316 Di Francesco, P., Guitter, E. and Jacobsen, J. L. Exact meander asymptotics: 
               a numerical check. Nuclear Phys. B 580 (2000), no. 3, 757-795.
%D A005316 Franz, Reinhard O. W. A partial order for the set of meanders. Ann. Comb. 
               2 (1998), no. 1, 7-18.
%D A005316 Franz, Reinhard O. W. and Earnshaw, Berton A. A constructive enumeration 
               of meanders. Ann. Comb. 6 (2002), no. 1, 7-17.
%D A005316 Isakov, N. M. and Yarmolenko, V. I. Bounded meander approximations. (Russian) 
               Qualitative and approximate methods for the investigation of operator 
               equations (Russian), 71-76, 162, Yaroslav. Gos. Univ., 1981.
%D A005316 I. Jensen and A. J. Guttmann, Critical exponents of plane meanders. J. 
               Phys. A 33, L187-L192 (2000).
%D A005316 Lando, S. K. and Zvonkin, A. K. Plane and projective meanders. Conference 
               on Formal Power Series and Algebraic Combinatorics (Bordeaux, 1991). 
               Theoret. Comput. Sci. 117 (1993), no. 1-2, 227-241.
%D A005316 Lando, S. K. and Zvonkin, A. K. Meanders. In Selected translations. Selecta 
               Math. Soviet. 11 (1992), no. 2, 117-144.
%D A005316 Makeenko, Y., Strings, matrix models and meanders. Theory of elementary 
               particles (Buckow, 1995). Nuclear Phys. B Proc. Suppl. 49 (1996), 
               226-237.
%D A005316 A. Phillips, Simple Alternating Transit Mazes, unpublished. 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 A005316 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 A005316 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005316 I. Jensen, <a href="b005316.txt">Table of n, a(n) for n = 0..43</a> [from 
               link below]
%H A005316 P. Di Francesco, O. Golinelli and E. Guitter, <a href="http://arXiv.org/
               abs/hep-th/9506030">Meander, folding and arch statistics</a>, Combinatorics 
               and physics (Marseilles, 1995). Math. Comput. Modelling 26 (1997), 
               no. 8-10, 97-147.
%H A005316 Di Francesco, P., Golinelli, O. and Guitter, E., <a href="http://arXiv.org/
               abs/cond-mat/9910453">Meanders: exact asymptotics</a>, Nuclear Phys. 
               B 570 (2000), no. 3, 699-712.
%H A005316 Di Francesco, P., Golinelli, O. and Guitter, E., <a href="http://arXiv.org/
               abs/hep-th/9607039">Meanders: a direct enumeration approach</a>, 
               Nuclear Phys. B 482 (1996), no. 3, 497-535.
%H A005316 I. Jensen, <a href="http://www.ms.unimelb.edu.au/~iwan/">Home page</a>
%H A005316 I. Jensen, <a href="http://arXiv.org/abs/cond-mat/0008178">A transfer 
               matrix approach to the enumeration of plane meanders</a>, J. Phys. 
               A 33 (2000), no. 34, 5953-5963.
%H A005316 I. Jensen, <a href="http://arXiv.org/cond-mat/9910313">Enumeration of 
               plane meanders</a>
%H A005316 I. Jensen, <a href="http://www.ms.unimelb.edu.au/~iwan/animals/series/
               open.meanders.ser">First 43 terms</a>
%H A005316 A. Phillips, <a href="http://www.math.sunysb.edu/~tony/mazes/index.html">
               Mazes</a>
%H A005316 A. Phillips, <a href="http://www.math.sunysb.edu/~tony/mazes/satmaze.html">
               Simple, Alternating, Transit Mazes</a>
%H A005316 N. J. A. Sloane, <a href="a5316.jpg">Illustration of initial terms</a>
%H A005316 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 A005316 M. La Croix, <a href="http://www.math.uwaterloo.ca/~malacroi/Latex/Meanders.pdf">
               Approaches to the Enumerative Theory of Meanders</a> [From Gerald 
               McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 26 2008]
%Y A005316 a(2n) is A005315. Cf. A076875, A076906, A076907, A077014, A077054, A077055, 
               A077056, A078591.
%Y A005316 See also A078592.
%Y A005316 Sequence in context: A080877 A007165 A107321 this_sequence A076876 A124495 
               A007919
%Y A005316 Adjacent sequences: A005313 A005314 A005315 this_sequence A005317 A005318 
               A005319
%K A005316 nonn,nice
%O A005316 0,4
%A A005316 N. J. A. Sloane (njas(AT)research.att.com), legendre(AT)biologie.ens.fr 
               (Stephane LEGENDRE)
%E A005316 Computed to n = 43 by Iwan Jensen.