login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319719 Number of non-isomorphic connected antichains of multisets of weight n. 24
1, 1, 3, 4, 10, 14, 48, 95, 305, 822, 2615 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In an antichain, no part is a proper submultiset of any other. The weight of an antichain is the sum of sizes of its parts. Weight is generally not the same as number of vertices. Connected antichains are also called clutters.

LINKS

Table of n, a(n) for n=0..10.

Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, Journal of Integer Sequences, Vol. 7 (2004).

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(4) = 10 connected antichains:

1: {{1}}

2: {{1,1}}

   {{1,2}}

   {{1},{1}}

3: {{1,1,1}}

   {{1,2,2}}

   {{1,2,3}}

   {{1},{1},{1}}

4: {{1,1,1,1}}

   {{1,1,2,2}}

   {{1,2,2,2}}

   {{1,2,3,3}}

   {{1,2,3,4}}

   {{1,1},{1,1}}

   {{1,2},{1,2}}

   {{1,2},{2,2}}

   {{1,3},{2,3}}

   {{1},{1},{1},{1}}

CROSSREFS

Cf. A001055, A001970, A007716, A007718, A056156, A096827, A253249, A285573, A293994, A318099, A319557, A319616-A319646, A319721.

Sequence in context: A056516 A056517 A285042 * A347568 A048155 A242342

Adjacent sequences:  A319716 A319717 A319718 * A319720 A319721 A319722

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 26 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 17 12:30 EDT 2022. Contains 356189 sequences. (Running on oeis4.)