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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.
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%I #7 Jan 02 2015 21:02:00

%S 0,1,0,0,1,1,5,13,46,155,561,2068,7871,30586,121391,490196,2011422,

%T 8370698,35285987,150485667,648653910,2823402675,12400659846,

%U 54920758496,245126368841,1101983749921,4987538210079,22716326086134

%N 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.

%H G. Kuperberg, <a href="http://arxiv.org/abs/q-alg/9712003">Spiders for rank 2 Lie algebras</a>, arXiv:q-alg/9712003, 1997.

%H G. Kuperberg, <a href="http://projecteuclid.org/euclid.cmp/1104287237">Spiders for rank 2 Lie algebras</a>, Comm. Math. Phys. 180 (1996), 109-151.

%F 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.

%e 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.

%Y Cf. A060049, A059710.

%K easy,nonn

%O 2,7

%A _Greg Kuperberg_, Feb 15 2001