A060050 Number of irreducible nonpositively curved triangulations of an n-gon: All internal vertices have at valence at least 6 and no diagonals of the n-gon are allowed.

0, 1, 0, 0, 1, 1, 5, 13, 46, 155, 561, 2068, 7871, 30586, 121391, 490196, 2011422, 8370698, 35285987, 150485667, 648653910, 2823402675, 12400659846, 54920758496, 245126368841, 1101983749921, 4987538210079, 22716326086134

Offset

2,7

Links

Table of n, a(n) for n=2..29.

G. Kuperberg, Spiders for rank 2 Lie algebras, arXiv:q-alg/9712003, 1997.

G. Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. 180 (1996), 109-151.

Formula

The g.f. C(x) is derived from the g.f. B(x) of A060049 by B_1(x) = C_1(B_1(x))+x, where B_1(x) = B(x)/x and C_1(x) = C(x)/x.

Example

c(8) = 5 = 1+4. We can divide the octagon into 8 pie slices and we can split any pair of opposite radii of this triangulation into two triangles.

Crossrefs

Cf. A060049, A059710.

Sequence in context: A147396 A320877 A099972 * A217892 A194639 A152925

Adjacent sequences: A060047 A060048 A060049 * A060051 A060052 A060053

Keyword

easy,nonn

Author

Greg Kuperberg, Feb 15 2001

Status

approved