cp's OEIS Frontend

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

%I A008828 #36 Jul 23 2025 14:47:28
%S A008828 1,2,2,8,12,5,42,84,56,14,262,640,580,240,42,1828,5236,5894,3344,990,
%T A008828 132,13820,45164,60312,42840,17472,4004,429,110954,406012,624240,
%U A008828 529104,271240,85904,16016,1430,933458,3772008,6540510,6413784,3935238,1569984,405552,63648,4862
%N A008828 Triangle read by rows: T(n,k) = number of closed meander systems of order n with k<=n components.
%C A008828 A meander of order n has 2n bridges. For many more references, see A005315 and A005316.
%H A008828 Andrew Howroyd, <a href="/A008828/b008828.txt">Table of n, a(n) for n = 1..210</a>
%H A008828 Bertrand Duplantier and Emmanuel Guitter, <a href="https://arxiv.org/abs/2507.12203">Liouville Quantum Duality and Random Planar Maps</a>, arXiv:2507.12203 [math-ph], 2025. See p. 50.
%H A008828 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 A008828 Motohisa Fukuda, Ion Nechita, <a href="https://arxiv.org/abs/1609.02756">Enumerating meandric systems with large number of components</a>, arXiv preprint arXiv:1609.02756 [math.CO], 2016.
%H A008828 Iwan Jensen, <a href="http://arxiv.org/abs/cond-mat/9910313">Enumeration of plane meanders</a>, arXiv:cond-mat/9910313 [cond-mat.stat-mech], 1999.
%H A008828 Michael La Croix, <a href="http://www.math.uwaterloo.ca/~malacroi/Latex/Meanders.pdf">Approaches to the Enumerative Theory of Meanders</a> [_Gerald McGarvey_, Oct 26 2008]
%H A008828 Sergei K. Lando and Alexander 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)
%H A008828 Sergei K. Lando and Alexander 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 (1993) p. 232.
%e A008828 Triangle starts:
%e A008828    1;
%e A008828    2  2;
%e A008828    8 12  5;
%e A008828   42 84 56 14;
%e A008828   ...
%Y A008828 Columns include A005315, A006657, A006658. Diagonals include A000108 (Catalan numbers), A006659, A007746. Row sums are in A001246.
%K A008828 nonn,tabl,nice
%O A008828 1,2
%A A008828 D. Ivanov, S. K. Lando, A. K. Zvonkin ( LabRI, Bordeaux, France)
%E A008828 More terms from Pab Ter (pabrlos(AT)yahoo.com), May 10 2004
%E A008828 Edited by _Ralf Stephan_, Dec 29 2004
%E A008828 T(10,k)-T(20,k) from _Andrew Howroyd_, Nov 22 2015