

A000682


Semimeanders: number of ways a semiinfinite directed curve can cross a straight line n times.
(Formerly M1205 N0464)


11



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
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OFFSET

0,3


COMMENTS

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


REFERENCES

I. Jensen, A transfer matrix approach to the enumeration of plane meanders. J. Phys. A 33, 59535963 (2000).
I. Jensen and A. J. Guttmann, Critical exponents of plane meanders. J. Phys. A 33, L187L192 (2000).
J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135152.
W. F. Lunnon, A mapfolding problem, Math. Comp. 22 (1968), 193199.
A. Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949.
J. Sawada and R. Li, Stamp foldings, semimeanders, 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), 385398.


LINKS

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) 497535.
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


EXAMPLE

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


CROSSREFS

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


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane.


EXTENSIONS

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


STATUS

approved



