0,3

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

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

For additional references see 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.

B. Bobier and J. Sawada, A fast algorithm to generate open meandric systems and meanders, preprint, 2007.

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

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

I. 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, S\'{e}ries Formelles et Combinatoire Alg\'{e}brique. Laboratoire Bordelais de Recherche Informatique, Universit\'{e} 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-Lagu\"{e}, Les R\'{e}seaux (ou Graphes)}, M\'{e}morial des Sciences Math\'{e}matiques, Fasc. 18, Gauthier-Villars, Paris, 1926, p. 47.

I. Jensen, Table of n, a(n) for n = 0..24 [from link below]

R. Bacher, Meander algebras

P. Di Francesco, O. Golinelli and E. Guitter, Meander, folding and arch statistics.

Erich Friedman, Illustration of initial terms

I. Jensen, Home page

I. Jensen, More terms

I. Jensen, Enumeration of plane meanders

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

A. Phillips, Mazes

A. Phillips, Simple, Alternating, Transit Mazes

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

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 525

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

A column of triangle A008828.

Sequence in context: A013999 A130649 A054993 this_sequence A121635 A002874 A078592

Adjacent sequences: A005312 A005313 A005314 this_sequence A005316 A005317 A005318

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com), J. A. Reeds (reeds(AT)idaccr.org)

Computed to n = 24 by Iwan Jensen.