A006657 -id:A006657

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A008828

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

+10
10

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

(list; table; graph; refs; listen; history; text; internal format)

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:

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.

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

A006658

Closed meanders with 3 components and 2n bridges.
(Formerly M4014)

+10
1

5, 56, 580, 5894, 60312, 624240, 6540510, 69323910, 742518832, 8028001566, 87526544560, 961412790002, 10630964761766, 118257400015312, 1322564193698320, 14863191405246888, 167771227744292160, 1901345329566422790

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,1

REFERENCES

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.

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

LINKS

Table of n, a(n) for n=3..20.

P. Di Francesco, O. Golinelli and E. Guitter, Meander, folding and arch statistics, arXiv:hep-th/9506030, 1995.

MATHEMATICA

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

a[n_] := A008828[[(n^2 - n + 6)/2]];

a /@ Range[3, 20] (* Jean-François Alcover, Sep 25 2019 *)

CROSSREFS

Cf. A005315, A006657.

A column of triangle A008828.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(13)-a(20) from Andrew Howroyd, Nov 22 2015

STATUS

approved

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