A005501 Number of unrooted triangulations of a pentagon with n internal nodes. (Formerly M3488)

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

Offset

0,2

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

Formula

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

Crossrefs

Column k=2 of the array in A169808.

Cf. A002711, A005506.

Sequence in context: A014512 A274804 A294222 * A065606 A049372 A050549

Adjacent sequences: A005498 A005499 A005500 * A005502 A005503 A005504

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved