cp's OEIS Frontend

A318132 Number of non-isomorphic set-systems (finite sets of finite nonempty sets) with union {1,2,...,n} and intersection {}.

%I A318132 #9 Jan 29 2024 13:48:38
%S A318132 1,0,2,26,1884,18660728,12813206113141264,
%T A318132 33758171486592987125648226573752576,
%U A318132 1435913805026242504952006868879460423733630400489039411798068453617852416
%N A318132 Number of non-isomorphic set-systems (finite sets of finite nonempty sets) with union {1,2,...,n} and intersection {}.
%H A318132 Andrew Howroyd, <a href="/A318132/b318132.txt">Table of n, a(n) for n = 0..12</a>
%F A318132 a(n) = A055621(n) - 2*A055621(n-1) = A000612(n) - 3*A000612(n-1) + 2*A000612(n-2) for n >= 2. - _Andrew Howroyd_, Jan 29 2024
%e A318132 Non-isomorphic representatives of the a(3) = 26 set-systems:
%e A318132   {{1},{2,3}}
%e A318132   {{1},{2},{3}}
%e A318132   {{1},{2},{1,3}}
%e A318132   {{1},{2},{1,2,3}}
%e A318132   {{1},{1,2},{2,3}}
%e A318132   {{1},{2,3},{1,2,3}}
%e A318132   {{1,2},{1,3},{2,3}}
%e A318132   {{1},{2},{3},{1,2}}
%e A318132   {{1},{2},{3},{1,2,3}}
%e A318132   {{1},{2},{1,2},{1,3}}
%e A318132   {{1},{2},{1,3},{2,3}}
%e A318132   {{1},{2},{1,2},{1,2,3}}
%e A318132   {{1},{2},{1,3},{1,2,3}}
%e A318132   {{1},{1,2},{1,3},{2,3}}
%e A318132   {{1},{1,2},{2,3},{1,2,3}}
%e A318132   {{1},{2},{3},{1,2},{1,3}}
%e A318132   {{1,2},{1,3},{2,3},{1,2,3}}
%e A318132   {{1},{2},{3},{1,2},{1,2,3}}
%e A318132   {{1},{2},{1,2},{1,3},{2,3}}
%e A318132   {{1},{2},{1,2},{1,3},{1,2,3}}
%e A318132   {{1},{2},{1,3},{2,3},{1,2,3}}
%e A318132   {{1},{1,2},{1,3},{2,3},{1,2,3}}
%e A318132   {{1},{2},{3},{1,2},{1,3},{2,3}}
%e A318132   {{1},{2},{3},{1,2},{1,3},{1,2,3}}
%e A318132   {{1},{2},{1,2},{1,3},{2,3},{1,2,3}}
%e A318132   {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%t A318132 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]]}]])]];
%t A318132 Table[Length[Union[sysnorm/@Select[Subsets[Rest[Subsets[Range[n]]]],And[Union@@#===Range[n],Intersection@@#=={}]&]]],{n,4}]
%Y A318132 Cf. A000371, A000612, A003465, A055621, A119563, A131288, A283877, A293606, A304997.
%Y A318132 Cf. A318128, A318129, A318130, A318131.
%K A318132 nonn
%O A318132 0,3
%A A318132 _Gus Wiseman_, Aug 18 2018
%E A318132 a(5) onwards from _Andrew Howroyd_, Jan 29 2024