A002713 Number of unrooted triangulations of the disk with n interior nodes and 3 nodes on the boundary.

1, 1, 1, 4, 16, 78, 457, 2938, 20118, 144113, 1065328, 8068332, 62297808, 488755938, 3886672165, 31269417102, 254141551498, 2084129777764, 17228043363781, 143432427097935, 1201853492038096, 10129428318995227, 85826173629557200

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

These are also called [n,0]-triangulations.

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• 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
• W. G. Brown, Enumeration of triangulations of the disk, Proc. London Math. Soc., 14 (1964), 746-768.
• W. G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768. [Annotated scanned copy]
• CombOS - Combinatorial Object Server, generate planar graphs
• 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)

Crossrefs

Column k=0 of A169808.

Formula

a(n) = (A002709(n) + A002712(n)) / 2.

Extensions

Terms a(9) onward from Max Alekseyev, May 11 2010

Name clarified by Andrew Howroyd, Feb 24 2021