A060049 Triangulations of an n-gon such that each internal vertex has valence at least 6, i.e., nonpositively curved triangulations.

1, 0, 1, 1, 2, 5, 15, 50, 181, 697, 2821, 11892, 51874, 232974, 1073070, 5053029, 24264565, 118570292, 588567257, 2963358162, 15114174106, 78004013763, 406971280545, 2144659072330, 11407141925639, 61197287846831

Offset: 0

Author

Greg Kuperberg, Feb 15 2001

Keywords

• easy
• nonn

Comments

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

Examples

			a(6) = 15 because there are 14 = A000108(4) triangulations without internal vertices, plus the triangulation with 6 pie slices.
		

Links

• Bruce Westbury, Table of n, a(n) for n = 0..39
• Greg Kuperberg, Spiders for rank 2 Lie algebras, arXiv:q-alg/9712003, 1997.
• Greg Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. 180 (1996), 109-151.
• Bruce W. Westbury, Enumeration of non-positive planar trivalent graphs, arXiv:math/0507112 [math.CO], 2005.
• Bruce W. Westbury, Enumeration of non-positive planar trivalent graphs, J. Algebraic Combin. 25 (2007)

Crossrefs

Cf. A059710.

Formula

The g.f. B(x) is derived from the g.f. A(x) of A059710 by A(x) = A(x*B(x))+1.