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A318531 Number of finite sets of set partitions of {1,...,n} such that any two have join {{1,...,n}}. 2
2, 4, 18, 450, 436270 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

The a(3) = 18 sets of set partitions:

        0

    {{1,2,3}}

   {{1,3},{2}}

   {{1,2},{3}}

   {{1},{2,3}}

  {{1},{2},{3}}

   {{1,3},{2}}   {{1,2,3}}

   {{1,2},{3}}   {{1,2,3}}

   {{1,2},{3}}  {{1,3},{2}}

   {{1},{2,3}}   {{1,2,3}}

   {{1},{2,3}}  {{1,3},{2}}

   {{1},{2,3}}  {{1,2},{3}}

  {{1},{2},{3}}  {{1,2,3}}

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

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

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

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

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

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]]]];

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];

Table[Length[stableSets[sps[Range[n]], Length[csm[Union[#1, #2]]]>1&]], {n, 4}]

CROSSREFS

Cf. A000110, A000258, A008277, A059849, A060639, A096827, A181939.

Cf. A318389, A318390, A318391, A318392, A318394, A318532.

Sequence in context: A347514 A306193 A323702 * A009667 A009508 A275000

Adjacent sequences:  A318528 A318529 A318530 * A318532 A318533 A318534

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 28 2018

STATUS

approved

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Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)