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 A060049 Triangulations of an n-gon 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 (list; graph; refs; listen; history; text; internal format)
 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: 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

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Last modified November 18 15:55 EST 2018. Contains 317323 sequences. (Running on oeis4.)