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

0,5

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

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)

Formula

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

Example

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

Crossrefs

Cf. A059710.

Sequence in context: A337526 A346661 A380748 * A107590 A245311 A148367

Adjacent sequences: A060046 A060047 A060048 * A060050 A060051 A060052

Keyword

easy,nonn

Author

Greg Kuperberg, Feb 15 2001

Status

approved