A317795 Number of non-isomorphic set-systems spanning n vertices with no singletons.

1, 0, 1, 6, 172, 611852, 200253853704512, 263735716028826427334553305221120, 5609038300883759793482640992086670066496449147691597380832361377955840

Offset

0,4

Links

Table of n, a(n) for n=0..8.

Example

Non-isomorphic representatives of the a(3) = 6 set-systems:
  {123}
  {12}{13}
  {12}{123}
  {12}{13}{23}
  {12}{13}{123}
  {12}{13}{23}{123}

Mathematica

sysnorm[{}]:={}; 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[Select[Subsets[Range[n]], Length[#]>1&]], Union@@#==Range[n]&]]], {n, 4}]

Crossrefs

First differences of A317794.

Cf. A000088, A000612, A003180, A007716, A055621, A283877, A300913, A306005, A317533, A317757, A319876.

Sequence in context: A266852 A266311 A323820 * A166762 A323279 A214801

Adjacent sequences: A317792 A317793 A317794 * A317796 A317797 A317798

Keyword

nonn

Author

Gus Wiseman, Aug 07 2018

Extensions

More terms from Gus Wiseman, Dec 13 2018

Status

approved