A001928 Number of connected topologies with n unlabeled nodes.

1, 1, 2, 6, 21, 94, 512, 3485, 29515, 314474, 4255727, 73831813, 1653083021, 47941962135, 1803010446411, 87882300251730, 5543501326580737

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more

References

• K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.
• 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).
• J. A. Wright, There are 718 6-point topologies, quasi-orderings and transgraphs, Notices Amer. Math. Soc., 17 (1970), p. 646, Abstract #70T-A106.
• J. A. Wright, personal communication.

Links

• K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184
• K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184. [Annotated scan of pages 180 and 183 only]
• P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
• Henry Sharp, Jr., Quasi-orderings and topologies on finite sets, Proceedings of the American Mathematical Society 17.6 (1966): 1344-1349. [Annotated scanned copy]
• N. J. A. Sloane, List of sequences related to partial orders, circa 1972
• J. A. Wright, There are 718 6-point topologies, quasiorderings and transgraphs, Preprint, 1970 [Annotated scanned copy]
• J. A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences

Crossrefs

Cf. A001929, A001930.

Programs

Mathematica

A001930 = Cases[Import["https://oeis.org/A001930/b001930.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{1} ~Join~ EulerInvTransform[Rest[A001930]] (* Jean-François Alcover, Jan 01 2020, updated Mar 17 2020 *)

Formula

Inverse Euler transform of A001930. - Vladeta Jovovic, Jan 06 2006

Extensions

More terms from Vladeta Jovovic, Jan 06 2006