login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306505 Number of non-isomorphic antichains of nonempty subsets of {1,...,n}. 11
1, 2, 4, 9, 29, 209, 16352, 490013147 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The spanning case is A006602 or A261005. The labeled case is A014466.

From Gus Wiseman, Jul 02 2019: (Start)

Also the number of unlabeled maximal antichains of nonempty subsets of {1..(n + 1)}. For example, non-isomorphic representatives of the a(0) = 1 through a(3) = 9 antichains are:

  {1}  {12}    {123}         {1234}

       {1}{2}  {1}{23}       {1}{234}

               {1}{2}{3}     {1}{2}{34}

               {12}{13}{23}  {1}{2}{3}{4}

                             {12}{134}{234}

                             {1}{23}{24}{34}

                             {12}{13}{14}{234}

                             {123}{124}{134}{234}

                             {12}{13}{14}{23}{24}{34}

(End)

LINKS

Table of n, a(n) for n=0..7.

Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

FORMULA

a(n) = A003182(n) - 1.

Partial sums of A006602 minus 1.

EXAMPLE

Non-isomorphic representatives of the a(0) = 1 through a(3) = 9 antichains:

  {}  {}     {}         {}

      {{1}}  {{1}}      {{1}}

             {{1,2}}    {{1,2}}

             {{1},{2}}  {{1},{2}}

                        {{1,2,3}}

                        {{1},{2,3}}

                        {{1},{2},{3}}

                        {{1,3},{2,3}}

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

CROSSREFS

Cf. A000372, A003182, A006126, A006602, A014466, A261005, A293606, A293993, A304996, A305000, A305001, A305857, A317674, A319721, A320449, A321679.

Cf. A007363, A306007, A307249, A326358, A326359, A326360, A326363.

Sequence in context: A300491 A229686 A208965 * A243789 A214935 A092329

Adjacent sequences:  A306502 A306503 A306504 * A306506 A306507 A306508

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Feb 20 2019

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 19:46 EST 2020. Contains 331030 sequences. (Running on oeis4.)