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Number of closed meanders with 2 components and 2n bridges.
(Formerly M2037)
2

%I M2037 #32 Jun 17 2022 12:24:48

%S 2,12,84,640,5236,45164,406012,3772008,35994184,351173328,3490681428,

%T 35253449296,360946635312,3739935635756,39159200588780,

%U 413836299216608,4409705753032648,47337525317450816,511563350415103008

%N Number of closed meanders with 2 components and 2n bridges.

%D S. K. Lando and A. K. Zvonkin "Plane and projective meanders", Séries Formelles et Combinatoire Algébrique. Laboratoire Bordelais de Recherche Informatique, Université Bordeaux I, 1991, pp. 287-303.

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

%H P. Di Francesco, O. Golinelli and E. Guitter, <a href="http://arXiv.org/abs/hep-th/9506030">Meander, folding and arch statistics</a>, arXiv:hep-th/9506030, 1995.

%H S. K. Lando and A. K. Zvonkin, <a href="/A005316/a005316_1.pdf">Plane and projective meanders</a>, Séries Formelles et Combinatoire Algébrique. Laboratoire Bordelais de Recherche Informatique, Université Bordeaux I, 1991, pp. 287-303. (Annotated scanned copy)

%t A008828 = Import["https://oeis.org/A008828/b008828.txt", "Table"][[All, 2]];

%t a[n_] := A008828[[(n^2 - n + 4)/2]];

%t a /@ Range[2, 20] (* _Jean-François Alcover_, Sep 25 2019 *)

%Y Cf. A005315.

%Y A column of triangle A008828.

%K nonn,nice

%O 2,1

%A _N. J. A. Sloane_, _Simon Plouffe_

%E a(13)-a(20) from _Andrew Howroyd_, Nov 22 2015