A005504 - OEIS

A005504

Number of unrooted triangulations of a disk with 2 internal nodes and n+3 nodes on the boundary.
(Formerly M3846)

1, 5, 14, 53, 178, 685, 2548, 9876, 37950, 147520, 572594, 2230735, 8693932, 33939465, 132598484, 518607032, 2029990774, 7952788446, 31179668572, 122331725930, 480283816348, 1886829349570, 7416950176904, 29171683995320, 114795961678380, 451968102200966, 1780298693036010

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

These are also called [2,n]-triangulations.

Graphs can be enumerated and counted using the tool "plantri", in particular the command "./plantri -s -P[n] -c2m2 [n+2]". - 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..500

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

Row n=2 of the array in A169808.

Sequence in context: A091218 A197601 A133751 * A146746 A073541 A268887

Adjacent sequences: A005501 A005502 A005503 * A005505 A005506 A005507

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(6)-a(12) from Manfred Scheucher, Mar 08 2018

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

STATUS

approved