A002713 Number of unrooted triangulations of the disk with n interior nodes and 3 nodes on the boundary. (Formerly M3524 N1431)

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

Offset

0,4

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)

Formula

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

Crossrefs

Column k=0 of A169808.

Sequence in context: A138294 A014514 A000780 * A221763 A362750 A356406

Adjacent sequences: A002710 A002711 A002712 * A002714 A002715 A002716

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Name clarified by Andrew Howroyd, Feb 24 2021

Status

approved