A330196 Number of unlabeled set-systems covering n vertices with no endpoints.

1, 0, 1, 20, 1754

Offset

0,4

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) = 20 set-systems:
  {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

First differences of the non-covering version A330124.

The "multi" version is A302545.

Unlabeled set-systems with no endpoints counted by vertices are A317794.

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

Unlabeled set-systems counted by vertices are A000612.

Unlabeled set-systems counted by weight are A283877.

Cf. A007716, A016031, A306005, A317795, A320665, A330052, A330053, A330055.

Sequence in context: A177296 A177297 A014606 * A172556 A246619 A222973

Adjacent sequences: A330193 A330194 A330195 * A330197 A330198 A330199

Keyword

nonn,more

Author

Gus Wiseman, Dec 05 2019

Status

approved