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A318131 Number of non-isomorphic sets of finite (possibly empty) sets with union {1,2,...,n} and intersection {}. 4
1, 1, 6, 60, 3836 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..4.

EXAMPLE

Non-isomorphic representatives of the a(2) = 6 sets of sets:

  {{1},{2}}

  {{},{1,2}}

  {{},{1},{2}}

  {{},{1},{1,2}}

  {{1},{2},{1,2}}

  {{},{1},{2},{1,2}}

MATHEMATICA

sysnorm[m_]:=If[Union@@m!=Range[Max@@Flatten[m]], sysnorm[m/.Rule@@@Table[{(Union@@m)[[i]], i}, {i, Length[Union@@m]}]], First[Sort[sysnorm[m, 1]]]]; sysnorm[m_, aft_]:=If[Length[Union@@m]<=aft, {m}, With[{mx=Table[Count[m, i, {2}], {i, Select[Union@@m, #>=aft&]}]}, Union@@(sysnorm[#, aft+1]&/@Union[Table[Map[Sort, m/.{par+aft-1->aft, aft->par+aft-1}, {0, 1}], {par, First/@Position[mx, Max[mx]]}]])]];

Table[Length[Union[sysnorm/@Select[Subsets[Subsets[Range[n]]], And[Union@@#===Range[n], Intersection@@#=={}]&]]], {n, 4}]

CROSSREFS

Cf. A000371, A003465, A119563, A131288, A283877, A293606, A304997.

Cf. A318128, A318129, A318130, A318132.

Sequence in context: A082681 A061431 A261523 * A202620 A075069 A324200

Adjacent sequences:  A318128 A318129 A318130 * A318132 A318133 A318134

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 18 2018

STATUS

approved

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)