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

1,2

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..210

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.

I. Jensen, Enumeration of plane meanders, arXiv:cond-mat/9910313 [cond-mat.stat-mech], 1999.

M. La Croix, Approaches to the Enumerative Theory of Meanders [Gerald McGarvey, Oct 26 2008]

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. (Annotated scanned copy)

S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Theoretical Computer Science Vol. 117 (1993) p. 232.

Example

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

Crossrefs

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

Sequence in context: A288053 A288506 A046690 * A254219 A053414 A189837

Adjacent sequences: A008825 A008826 A008827 * A008829 A008830 A008831

Keyword

nonn,tabl,nice

Author

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

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

Status

approved