OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..12
FORMULA
EXAMPLE
Non-isomorphic representatives of the a(3) = 26 set-systems:
{{1},{2,3}}
{{1},{2},{3}}
{{1},{2},{1,3}}
{{1},{2},{1,2,3}}
{{1},{1,2},{2,3}}
{{1},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1},{2},{3},{1,2}}
{{1},{2},{3},{1,2,3}}
{{1},{2},{1,2},{1,3}}
{{1},{2},{1,3},{2,3}}
{{1},{2},{1,2},{1,2,3}}
{{1},{2},{1,3},{1,2,3}}
{{1},{1,2},{1,3},{2,3}}
{{1},{1,2},{2,3},{1,2,3}}
{{1},{2},{3},{1,2},{1,3}}
{{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{1,2},{1,2,3}}
{{1},{2},{1,2},{1,3},{2,3}}
{{1},{2},{1,2},{1,3},{1,2,3}}
{{1},{2},{1,3},{2,3},{1,2,3}}
{{1},{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{1,2},{1,3},{2,3}}
{{1},{2},{3},{1,2},{1,3},{1,2,3}}
{{1},{2},{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
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[Rest[Subsets[Range[n]]]], And[Union@@#===Range[n], Intersection@@#=={}]&]]], {n, 4}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 18 2018
EXTENSIONS
a(5) onwards from Andrew Howroyd, Jan 29 2024
STATUS
approved