A005502 Number of unrooted triangulations of a hexagon with n internal nodes. (Formerly M2904)

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

Offset

0,1

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

Formula

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

Crossrefs

Column k=3 of the array in A169808.

Cf. A005507, A005495.

Sequence in context: A053557 A039302 A074512 * A305710 A351200 A000255

Adjacent sequences: A005499 A005500 A005501 * A005503 A005504 A005505

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved