0,3

There is a 1-to-1 correspondence between loops crossing a road 2n times and lines crossing a road 2n-1 times.

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.

B. Bobier and J. Sawada, A fast algorithm to generate open meandric systems and meanders, ACM Transactions on Algorithms, Vol. 6, No. 2, 2010, article #42.

Franz, Reinhard O. W. and Earnshaw, Berton A. A constructive enumeration of meanders. Ann. Comb. 6 (2002), no. 1, 7-17.

Iwan Jensen, A transfer matrix approach to the enumeration of plane meanders. J. Phys. A 33, 5953-5963 (2000).

Iwan Jensen and A. J. Guttmann, Critical exponents of plane meanders. J. Phys. A 33, L187-L192 (2000).

S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Séries Formelles et Combinatoire Algébrique. Laboratoire Bordelais de Recherche Informatique, Université Bordeaux I, 1991, pp. 287-303.

S. K. Lando and A. K. Zvonkin, Meanders, Selecta Mathematica Sovietica, Vol. 11, Number 2, pp. 117-144, 1992.

S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Theoretical Computer Science Vol. 117, p227-241, 1993.

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.

V. R. Pratt, personal communication.

J. A. Reeds and L. A. Shepp, An upper bound on the meander constant, preprint, May 25, 1999. [Obtains upper bound of 13.01]

M. A. Sainte-Laguë, Les Réseaux (ou Graphes), Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1926, p. 47.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

For additional references see A005316.

Iwan Jensen and Andrew Howroyd, Table of n, a(n) for n = 0..28 (first 24 terms from I. Jensen)

R. Bacher, Meander algebras

David Bevan, Random Closed Meanders - David Bevan, Jun 25 2010

P. Di Francesco, O. Golinelli and E. Guitter, Meander, folding and arch statistics, arXiv:hep-th/9506030, 1995.

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, 2009; see page 525

Erich Friedman, Illustration of initial terms

Iwan Jensen, Home page

Iwan Jensen, Closed meanders, a(n) for n = 1..24

Iwan Jensen, Enumeration of plane meanders, arXiv:cond-mat/9910313 [cond-mat.stat-mech], 1999.

Michael La Croix, Approaches to the Enumerative Theory of Meanders, 2003.

S. K. Lando and A. K. Zvonkin , Plane and projective meanders, Séries Formelles et Combinatoire Algébrique. Laboratoire Bordelais de Recherche Informatique, Université Bordeaux I, 1991, pp. 287-303. (Annotated scanned copy)

A. Panayotopoulos and P. Tsikouras, Meanders and Motzkin Words, J. Integer Seqs., Vol. 7, 2004.

A. Phillips, Mazes

A. Phillips, Simple, Alternating, Transit Mazes

J. A. Reeds, D. E. Knuth, & N. J. A. Sloane, Email Correspondence

J. Reeds, L. Shepp, & D. McIlroy, Numerical bounds for the Arnol'd "meander" constant, Preprint.

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

a(n) = A005316(2n-1).

These are the odd-numbered terms of A005316. Cf. A077054. For nonisomorphic solutions see A077460.

A column of triangle A008828.

Sequence in context: A054993 A188912 A229285 * A182520 A121635 A002874

Adjacent sequences:  A005312 A005313 A005314 * A005316 A005317 A005318

nonn,hard,nice

N. J. A. Sloane, J. A. Reeds (reeds(AT)idaccr.org)

approved