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A000682 Semimeanders: number of ways a semi-infinite directed curve can cross a straight line n times.
(Formerly M1205 N0464)
1, 1, 2, 4, 10, 24, 66, 174, 504, 1406, 4210, 12198, 37378, 111278, 346846, 1053874, 3328188, 10274466, 32786630, 102511418, 329903058, 1042277722, 3377919260, 10765024432, 35095839848, 112670468128, 369192702554, 1192724674590, 3925446804750 (list; graph; refs; listen; history; text; internal format)



Number of ways to fold a strip of n+1 labeled stamps with leaf 1 on top. [Clarified by Stéphane Legendre, Apr 09 2013]


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).

J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152.

W. F. Lunnon, A map-folding problem, Math. Comp. 22 (1968), 193-199.

A. Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949.

J. Sawada and R. Li, Stamp foldings, semi-meanders, and open meanders: fast generation algorithms, Electronic Journal of Combinatorics, Volume 19 No. 2 (2012), P#43 (16 pages).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

J. Touchard, Contributions a` l'e'tude du proble`me des timbres postes, Canad. J. Math., 2 (1950), 385-398.


I. Jensen, Table of n, a(n) for n = 1..45

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

P. Di Francesco, O. Golinelli and E. Guitter, Meanders: a direct enumeration approach, Nucl. Phys. B 482 [ FS ] (1996) 497-535.

P. Di Francesco, Matrix model combinatorics: applications to folding and coloring

I. Jensen, Home page

I. Jensen, Terms a(1)..a(45)

M. La Croix, Approaches to the Enumerative Theory of Meanders

Stéphane Legendre, Foldings and Meanders, arXiv preprint arXiv:1302.2025, 2013.

Stéphane Legendre, Illustration of initial terms

Index entries for sequences obtained by enumerating foldings


a(3) = 4: the four solutions with three crossings are the two solutions shown in A086441 together with their reflections about a North-South axis.


A000560(n) = a(n)/2 (for n >= 2) gives number of nonisomorphic solutions (see also A086441). Cf. A001011, A001997.

Sequence in context: A084078 A137842 A049146 * A001997 A239605 A000084

Adjacent sequences:  A000679 A000680 A000681 * A000683 A000684 A000685




N. J. A. Sloane.


Sade gives the first 11 terms. Computed to n = 45 by Iwan Jensen.



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Last modified April 19 17:18 EDT 2014. Contains 240762 sequences.