A008828 Triangle read by rows: T(n,k) = number of closed meander systems of order n with k<=n components.

1, 2, 2, 8, 12, 5, 42, 84, 56, 14, 262, 640, 580, 240, 42, 1828, 5236, 5894, 3344, 990, 132, 13820, 45164, 60312, 42840, 17472, 4004, 429, 110954, 406012, 624240, 529104, 271240, 85904, 16016, 1430, 933458, 3772008, 6540510, 6413784, 3935238, 1569984, 405552, 63648, 4862

Offset: 1

Author

D. Ivanov, S. K. Lando, A. K. Zvonkin ( LabRI, Bordeaux, France)

Keywords

• nonn
• tabl
• nice

Comments

A meander of order n has 2n bridges. For many more references, see A005315 and A005316.

Examples

			Triangle starts:
   1;
   2  2;
   8 12  5;
  42 84 56 14;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..210
• Bertrand Duplantier and Emmanuel Guitter, Liouville Quantum Duality and Random Planar Maps, arXiv:2507.12203 [math-ph], 2025. See p. 50.
• P. Di Francesco, O. Golinelli and E. Guitter, Meander, folding and arch statistics, arXiv:hep-th/9506030, 1995.
• Motohisa Fukuda, Ion Nechita, Enumerating meandric systems with large number of components, arXiv preprint arXiv:1609.02756 [math.CO], 2016.
• Iwan Jensen, Enumeration of plane meanders, arXiv:cond-mat/9910313 [cond-mat.stat-mech], 1999.
• Michael La Croix, Approaches to the Enumerative Theory of Meanders [_Gerald McGarvey_, Oct 26 2008]
• Sergei K. Lando and Alexander K. Zvonkin, Plane and projective meanders, Séries Formelles et Combinatoire Algébrique. Laboratoire Bordelais de Recherche Informatique, Université Bordeaux I, 1991, pp. 287-303. (Annotated scanned copy)
• Sergei K. Lando and Alexander K. Zvonkin, Plane and projective meanders, Theoretical Computer Science Vol. 117 (1993) p. 232.

Crossrefs

Columns include A005315, A006657, A006658. Diagonals include A000108 (Catalan numbers), A006659, A007746. Row sums are in A001246.

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 10 2004

Edited by Ralf Stephan, Dec 29 2004

T(10,k)-T(20,k) from Andrew Howroyd, Nov 22 2015