A259974 Irregular triangle read by rows: T(n,k) = number of meanders with n bridges in which the first bridge is bridge k.
1, 1, 1, 1, 2, 1, 3, 2, 3, 8, 3, 3, 14, 7, 7, 14, 42, 14, 11, 14, 81, 36, 28, 36, 81, 262, 81, 57, 57, 81, 538, 221, 155, 155, 221, 538, 1828, 538, 353, 316, 353, 538, 3926, 1530, 1003, 902, 1003, 1530, 3926, 13820, 3926, 2458, 2053, 2053, 2458, 3926, 30694, 11510, 7214, 6059, 6059, 7214, 11510, 30694, 110954, 30694, 18575, 14810, 13827, 14810, 18575, 30694
Offset: 1
Examples
Triangle begins: 1, 1, 1,1, 2,1, 3,2,3, 8,3,3, 14,7,7,14, 42,14,11,14, 81,36,28,36,81, 262,81,57,57,81, 538,221,155,155,221,538, ...
References
- Lando, S. K. and Zvonkin, A. K. Plane and projective meanders. Conference on Formal Power Series and Algebraic Combinatorics (Bordeaux, 1991).
- Lando, S. K. and Zvonkin, A. K. Meanders. In Selected translations. Selecta Math. Soviet. 11 (1992), no. 2, 117-144.
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..420
- 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), no. 1-2, 227-241.
Extensions
T(12,k)-T(40,k) from Andrew Howroyd, Dec 15 2015