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%I #20 Jan 02 2015 21:12:23
%S 1,0,1,1,2,5,15,50,181,697,2821,11892,51874,232974,1073070,5053029,
%T 24264565,118570292,588567257,2963358162,15114174106,78004013763,
%U 406971280545,2144659072330,11407141925639,61197287846831
%N Triangulations of an n-gon such that each internal vertex has valence at least 6, i.e., nonpositively curved triangulations.
%C This is the connected version of A059710 in the following sense. Let C(x) be the ordinary generating function for this sequence and A(x) the ordinary generating function for A059710. Then these satisfy the functional equation A(x) = C(x*A(x)). - _Bruce Westbury_, Nov 05 2013
%H Bruce Westbury, <a href="/A060049/b060049.txt">Table of n, a(n) for n = 0..39</a>
%H Greg Kuperberg, <a href="http://arxiv.org/abs/q-alg/9712003">Spiders for rank 2 Lie algebras</a>, arXiv:q-alg/9712003, 1997.
%H Greg Kuperberg, <a href="http://projecteuclid.org/euclid.cmp/1104287237">Spiders for rank 2 Lie algebras</a>, Comm. Math. Phys. 180 (1996), 109-151.
%H Bruce W. Westbury, <a href="http://arxiv.org/abs/math/0507112">Enumeration of non-positive planar trivalent graphs</a>, arXiv:math/0507112 [math.CO], 2005.
%H Bruce W. Westbury, <a href="http://dx.doi.org/10.1007/s10801-006-0041-4">Enumeration of non-positive planar trivalent graphs</a>, J. Algebraic Combin. 25 (2007)
%F The g.f. B(x) is derived from the g.f. A(x) of A059710 by A(x) = A(x*B(x))+1.
%e a(6) = 15 because there are 14 = A000108(4) triangulations without internal vertices, plus the triangulation with 6 pie slices.
%Y Cf. A059710.
%K easy,nonn
%O 0,5
%A _Greg Kuperberg_, Feb 15 2001
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