A005501 Number of unrooted triangulations of a pentagon with n internal nodes.

1, 4, 14, 69, 396, 2503, 16905, 119571, 874771, 6567181, 50329363, 392328944, 3102523829, 24839151315, 201011560316, 1642124006250, 13527821578754, 112279051170871, 938188211057701, 7887160187935198, 66672792338916470, 566452703137103796, 4834838039006782636

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

These are also called [n,2]-triangulations.

Graphs can be enumerated and counted using the tool "plantri", in particular the command "./plantri -s -P5 -c2m2 [n]". - Manfred Scheucher, Mar 08 2018

References

• C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• G. Brinkmann and B. McKay, Plantri (program for generation of certain types of planar graph)
• C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979. (Annotated scanned copy)
• C. F. Earl & N. J. A. Sloane, Correspondence, 1980-1981

Crossrefs

Column k=2 of the array in A169808.

Cf. A002711, A005506.

Formula

a(n) = (A005506(n) + A002711(n))/2. - Max Alekseyev, Oct 29 2012

Extensions

a(6)-a(11) from Manfred Scheucher, Mar 08 2018

Name clarified and terms a(12) and beyond from Andrew Howroyd, Feb 22 2021