A005500 Number of unrooted triangulations of a quadrilateral with n internal nodes.

1, 2, 5, 18, 88, 489, 3071, 20667, 146381, 1072760, 8071728, 61990477, 484182622, 3835654678, 30757242535, 249255692801, 2038827903834, 16815060576958, 139706974995635, 1168468902294726, 9831504782276593, 83174244225508659, 707159273362126228, 6039827641569969225

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

These are also called [n,1]-triangulations.

Graphs can be enumerated and counted using the tool "plantri", in particular the command "./plantri -s -P4 -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=1 of A169808.

Cf. A002710, A005505.

Formula

a(n) = (A005505(n) + A002710(n))/2. - Max Alekseyev, Oct 29 2012

Extensions

Edited by Max Alekseyev, Oct 29 2012

a(7)-a(12) from Manfred Scheucher, Mar 08 2018

Name clarified and terms a(13) and beyond from Andrew Howroyd, Feb 22 2021