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A005315 Closed meandric numbers (or meanders): ways a loop can cross a road 2n times.
(Formerly M1862)
26
1, 1, 2, 8, 42, 262, 1828, 13820, 110954, 933458, 8152860, 73424650, 678390116, 6405031050, 61606881612, 602188541928, 5969806669034, 59923200729046, 608188709574124, 6234277838531806, 64477712119584604, 672265814872772972, 7060941974458061392 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

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.

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-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.

LINKS

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

R. Bacher, Meander algebras

David Bevan, Random Closed Meanders [From David Bevan, Jun 25 2010]

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

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

Erich Friedman, Illustration of initial terms

I. Jensen, Home page

I. Jensen, More terms

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

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

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).

CROSSREFS

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

KEYWORD

nonn,hard,more,nice,changed

AUTHOR

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

EXTENSIONS

Computed to n = 24 by Iwan Jensen.

STATUS

approved

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Last modified July 25 23:14 EDT 2014. Contains 244919 sequences.