A005503 Number of unrooted triangulations of a disk with one internal node and n+3 nodes on the boundary.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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

• 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.

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