A005502 Number of unrooted triangulations of a hexagon with n internal nodes.

3, 11, 53, 295, 1867, 12560, 89038, 652198, 4903955, 37627699, 293607612, 2323604832, 18614121391, 150704813812, 1231596828200, 10148762396401, 84252059397251, 704122279126074, 5920239345451780, 50051285956517452, 425273487358680290, 3630084126997807369

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

These are also called [n,3]-triangulations.

Graphs can be enumerated and counted using the tool "plantri", in particular the command "./plantri -s -P6 -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=3 of the array in A169808.

Cf. A005507, A005495.

Formula

a(n) = (A005507(n) + A005495(n))/2 (based on Max Alekseyev's formula, cf. A005501 and A005500).

Extensions

a(5)-a(10) from Manfred Scheucher, Mar 08 2018

Name clarified and terms a(11) and beyond from Andrew Howroyd, Feb 22 2021