A319637 - OEIS

A319637

Number of non-isomorphic T_0-covers of n vertices by distinct sets.

1, 1, 3, 29, 1885, 18658259

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OFFSET

0,3

COMMENTS

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The T_0 condition means the dual is strict (no repeated elements).

LINKS

Table of n, a(n) for n=0..5.

EXAMPLE

Non-isomorphic representatives of the a(3) = 29 covers:

{{1,3},{2,3}}

{{1},{2},{3}}

{{1},{3},{2,3}}

{{2},{3},{1,2,3}}

{{2},{1,3},{2,3}}

{{3},{1,3},{2,3}}

{{3},{2,3},{1,2,3}}

{{1,2},{1,3},{2,3}}

{{1},{2},{3},{2,3}}

{{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{1,2,3}}

{{1},{2},{1,3},{2,3}}

{{2},{3},{1,3},{2,3}}

{{1},{3},{2,3},{1,2,3}}

{{2},{3},{2,3},{1,2,3}}

{{3},{1,2},{1,3},{2,3}}

{{2},{1,3},{2,3},{1,2,3}}

{{3},{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{1,3},{2,3}}

{{1,2},{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{2,3},{1,2,3}}

{{2},{3},{1,2},{1,3},{2,3}}

{{1},{2},{1,3},{2,3},{1,2,3}}

{{2},{3},{1,3},{2,3},{1,2,3}}

{{3},{1,2},{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{1,2},{1,3},{2,3}}

{{1},{2},{3},{1,3},{2,3},{1,2,3}}

{{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

CROSSREFS

Cf. A006126, A007716, A049311, A059201, A283877, A316980, A316983, A318099, A319558, A319559, A319616-A319646, A300913.

Sequence in context: A162085 A182385 A255597 * A003190 A322451 A213792

Adjacent sequences: A319634 A319635 A319636 * A319638 A319639 A319640

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

EXTENSIONS

a(5) from Max Alekseyev, Jul 13 2022

STATUS

approved