%I A000682 M1205 N0464
%S A000682 1,1,2,4,10,24,66,174,504,1406,4210,12198,37378,111278,346846,1053874,
%T A000682 3328188,10274466,32786630,102511418,329903058,1042277722,3377919260,
%U A000682 10765024432,35095839848,112670468128,369192702554,1192724674590,3925446804750
%N A000682 Semimeanders: number of ways a semi-infinite directed curve can cross 
               a straight line n times.
%C A000682 Number of ways to fold a strip of n+1 labeled stamps.
%D A000682 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000682 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000682 I. Jensen, A transfer matrix approach to the enumeration of plane meanders. 
               J. Phys. A 33, 5953-5963 (2000).
%D A000682 I. Jensen and A. J. Guttmann, Critical exponents of plane meanders. J. 
               Phys. A 33, L187-L192 (2000).
%D A000682 J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 
               135-152.
%D A000682 W. F. Lunnon, A map-folding problem, Math. Comp. 22 (1968), 193-199.
%D A000682 A. Sade, Sur les Chevauchements des Permutations, published by the author, 
               Marseille, 1949.
%D A000682 J. Touchard, Contributions a` l'e'tude du proble`me des timbres postes, 
               Canad. J. Math., 2 (1950), 385-398.
%H A000682 I. Jensen, <a href="b000682.txt">Table of n, a(n) for n = 1..45</a>
%H A000682 P. Di Francesco, O. Golinelli and E. Guitter, <a href="http://arXiv.org/
               abs/hep-th/9506030">Meander, folding and arch statistics.</a>
%H A000682 P. Di Francesco, O. Golinelli and E. Guitter, <a href="http://arXiv.org/
               abs/hep-th/9607039">Meanders: a direct enumeration approach</a>, 
               Nucl. Phys. B 482 [ FS ] (1996) 497-535.
%H A000682 I. Jensen, <a href="http://www.ms.unimelb.edu.au/~iwan/">Home page</a>
%H A000682 I. Jensen, <a href="http://www.ms.unimelb.edu.au/~iwan/animals/series/
               semi.meanders.ser">More terms</a>
%H A000682 <a href="Sindx_Fo.html#fold">Index entries for sequences obtained by 
               enumerating foldings</a>
%H A000682 P. Di Francesco, <a href="http://arXiv.org/abs/math-ph/9911002">Matrix 
               model combinatorics: applications to folding and coloring</a>
%H A000682 M. La Croix, <a href="http://www.math.uwaterloo.ca/~malacroi/Latex/Meanders.pdf"> 
               Approaches to the Enumerative Theory of Meanders</a> [From Gerald 
               McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 26 2008]
%e A000682 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.
%Y A000682 A000560(n) = a(n)/2 (for n >= 2) gives number of nonisomorphic solutions 
               (see also A086441). Cf. A001011, A001997.
%Y A000682 Sequence in context: A084078 A137842 A049146 this_sequence A001997 A000084 
               A057734
%Y A000682 Adjacent sequences: A000679 A000680 A000681 this_sequence A000683 A000684 
               A000685
%K A000682 nonn,nice
%O A000682 0,3
%A A000682 N. J. A. Sloane (njas(AT)research.att.com).
%E A000682 Sade gives the first 11 terms. Computed to n = 45 by Iwan Jensen.