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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326565 Number of covering antichains of nonempty, non-singleton subsets of {1..n}, all having the same sum. 8
1, 0, 1, 1, 4, 13, 91, 1318, 73581, 51913025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

An antichain is a finite set of finite sets, none of which is a subset of any other. It is covering if its union is {1..n}. The edge-sums are the sums of vertices in each edge, so for example the edge sums of {{1,3},{2,5},{3,4,5}} are {4,7,12}.

LINKS

Table of n, a(n) for n=0..9.

EXAMPLE

The a(2) = 1 through a(5) = 13 antichains:

  {{1,2}}  {{1,2,3}}  {{1,2,3,4}}      {{1,2,3,4,5}}

                      {{1,4},{2,3}}    {{1,2,5},{1,3,4}}

                      {{2,4},{1,2,3}}  {{1,3,5},{2,3,4}}

                      {{3,4},{1,2,4}}  {{1,4,5},{2,3,5}}

                                       {{1,4,5},{1,2,3,4}}

                                       {{2,3,5},{1,2,3,4}}

                                       {{2,4,5},{1,2,3,5}}

                                       {{3,4,5},{1,2,4,5}}

                                       {{1,5},{2,4},{1,2,3}}

                                       {{2,5},{3,4},{1,2,4}}

                                       {{3,5},{1,2,5},{1,3,4}}

                                       {{4,5},{1,3,5},{2,3,4}}

                                       {{1,4,5},{2,3,5},{1,2,3,4}}

MATHEMATICA

stableSets[u_, Q_]:=If[Length[u]==0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r==w||Q[r, w]||Q[w, r]], Q]]]];

cleq[n_]:=Select[stableSets[Subsets[Range[n], {2, n}], SubsetQ[#1, #2]||Total[#1]!=Total[#2]&], Union@@#==Range[n]&];

Table[Length[cleq[n]], {n, 0, 5}]

CROSSREFS

Cf. A000372, A006126, A035470, A307249, A321455, A321717, A321718, A326360, A326518, A326534, A326566.

Sequence in context: A131590 A281182 A200850 * A041433 A222764 A058014

Adjacent sequences:  A326562 A326563 A326564 * A326566 A326567 A326568

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 13 2019

EXTENSIONS

a(9) from Andrew Howroyd, Aug 14 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 November 27 05:27 EST 2020. Contains 338678 sequences. (Running on oeis4.)