

A060049


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


3



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
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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:qalg/9712003, 1997.
Greg Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. 180 (1996), 109151.
Bruce W. Westbury, Enumeration of nonpositive planar trivalent graphs, arXiv:math/0507112 [math.CO], 2005.
Bruce W. Westbury, Enumeration of nonpositive 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: A279553 A007853 A149952 * A107590 A245311 A148367
Adjacent sequences: A060046 A060047 A060048 * A060050 A060051 A060052


KEYWORD

easy,nonn


AUTHOR

Greg Kuperberg, Feb 15 2001


STATUS

approved



