A005503 - OEIS

A005503

Number of unrooted triangulations of a disk with one internal node and n+3 nodes on the boundary.
(Formerly M1248)

1, 2, 4, 11, 28, 91, 291, 1004, 3471, 12350, 44114, 159519, 579835, 2121845, 7800702, 28813730, 106844383, 397647256, 1484755972, 5560561040, 20881939915, 78617991116, 296678132514, 1121988213996, 4251702739831, 16141719280994, 61389611762126, 233856524866209

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

OFFSET

0,2

COMMENTS

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

Graphs can be enumerated and counted using the tool "plantri", in particular the command "./plantri -s -P[n] -c2m2 [n+1]". - 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

Table of n, a(n) for n=0..27.

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=1 of the array in A169808.

Sequence in context: A148136 A148137 A148138 * A148139 A336871 A061860

Adjacent sequences: A005500 A005501 A005502 * A005504 A005505 A005506

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(6) corrected and a(7)-a(14) from Manfred Scheucher, Mar 08 2018

Name clarified and terms a(15) and beyond from Andrew Howroyd, Feb 22 2021

STATUS

approved