A005500 Number of unrooted triangulations of a quadrilateral with n internal nodes. (Formerly M1516)

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

0,2

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

Formula

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

Crossrefs

Column k=1 of A169808.

Cf. A002710, A005505.

Sequence in context: A142153 A287227 A094294 * A020025 A113715 A227094

Adjacent sequences: A005497 A005498 A005499 * A005501 A005502 A005503

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved