A330124 Number of unlabeled set-systems with n vertices and no endpoints.

1, 1, 2, 22, 1776

Offset

0,3

Comments

A set-system is a finite set of finite nonempty sets. An endpoint is a vertex appearing only once (degree 1).

Links

Table of n, a(n) for n=0..4.

Example

Non-isomorphic representatives of the a(3) = 22 set-systems:
  0
  {1}{2}{12}
  {12}{13}{23}
  {1}{23}{123}
  {12}{13}{123}
  {1}{2}{13}{23}
  {1}{2}{3}{123}
  {1}{12}{13}{23}
  {1}{2}{13}{123}
  {1}{12}{13}{123}
  {1}{12}{23}{123}
  {12}{13}{23}{123}
  {1}{2}{3}{12}{13}
  {1}{2}{12}{13}{23}
  {1}{2}{3}{12}{123}
  {1}{2}{12}{13}{123}
  {1}{2}{13}{23}{123}
  {1}{12}{13}{23}{123}
  {1}{2}{3}{12}{13}{23}
  {1}{2}{3}{12}{13}{123}
  {1}{2}{12}{13}{23}{123}
  {1}{2}{3}{12}{13}{23}{123}

Crossrefs

Partial sums of the covering case A330196.

The labeled version is A330059.

The "multi" version is A302545.

Unlabeled set-systems with no endpoints counted by weight are A330054.

Unlabeled set-systems with no singletons are A317794.

Unlabeled set-systems counted by vertices are A000612.

Unlabeled set-systems counted by weight are A283877.

The case with no singletons is A320665.

Cf. A007716, A016031, A306005, A317795, A321405, A330052, A330055.

Sequence in context: A193486 A337577 A054948 * A104149 A113761 A319620

Adjacent sequences: A330121 A330122 A330123 * A330125 A330126 A330127

Keyword

nonn,more

Author

Gus Wiseman, Dec 05 2019

Status

approved