A001928 Number of connected topologies with n unlabeled nodes. (Formerly M1655 N0648)

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

Offset

0,3

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

Table of n, a(n) for n=0..16.

Kim Ki-Hang Butler and George Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.

Kim Ki-Hang Butler and George 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]

Sangmin Chun, Gangyong Lee, Mauricio Medina-Barcenas, and Cosmin S. Roman, Rudimentary Structural Matrix Rings, J. Alg. Appl. (2026). See p. 13.

Peter J. Cameron, Sequences realized by oligomorphic permutation groups, J. Int. Seq. 3 (2000), Art. 00.1.5.

Henry Sharp, Jr., Quasi-orderings and topologies on finite sets, Proc. Amer. Math. Soc. 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.

Formula

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

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 *)

Crossrefs

Cf. A001929, A001930.

Sequence in context: A266328 A214087 A183950 * A005638 A249395 A008988

Adjacent sequences: A001925 A001926 A001927 * A001929 A001930 A001931

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Jan 06 2006

Status

approved