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Number of meanders of order 2n+1 (4*n+2 crossings of the infinite line) with central 1-1 cut.
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%I #27 Jun 10 2024 08:52:09

%S 4,64,1764,68644,3341584,190992400,12310790116,871343837764,

%T 66469126179600,5391179227622500,460213149486493456,

%U 41024422751464102500,3795407861954983718544,362631040029370613957184,35638591665642822414493156,3590789985613539065908070116,369893506453438150061450367376

%N Number of meanders of order 2n+1 (4*n+2 crossings of the infinite line) with central 1-1 cut.

%D Antonios Panayotopoulos and Panos Tsikouras, Properties of meanders, JCMCC 46 (2003), 181-190.

%D Antonios Panayotopoulos and Panayiotis Vlamos, Meandric Polygons, Ars Combinatoria 87 (2008), 147-159.

%H S. K. Lando and A. K. Zvonkin, <a href="http://dx.doi.org/10.1016/0304-3975(93)90316-L">Plane and projective meanders</a>, Theoretical Computer Science Vol. 117, pp. 227-241, 1993.

%H Antonios Panayotopoulos and Panos Tsikouras, <a href="https://doi.org/10.4000/msh.2808">The multimatching property of nested sets</a>, Math. & Sci. Hum. 149 (2000), 23-30.

%H Antonios Panayotopoulos and Panos Tsikouras, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Panayotopoulos/panayo4.html">Meanders and Motzkin Words</a>, J. Integer Seq., Vol. 7 (2004), Article 04.1.2.

%H Antonios Panayotopoulos and Panayiotis Vlamos, <a href="http://dx.doi.org/10.1007/978-3-642-33412-2_49">Cutting Degree of Meanders</a>, Artificial Intelligence Applications and Innovations, IFIP Advances in Information and Communication Technology, Volume 382, 2012, pp 480-489; DOI 10.1007/978-3-642-33412-2_49. - From _N. J. A. Sloane_, Dec 29 2012

%F a(n) = A005315(n+1)^2.

%Y Cf. A005315, A192927, A207851.

%K nonn

%O 1,1

%A _Panayotis Vlamos_ and _Antonios Panayotopoulos_, Feb 25 2012

%E More terms using the data at A005315 added by _Amiram Eldar_, Jun 09 2024