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
Examples
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.
Links
- 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.