OFFSET
0,3
COMMENTS
An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge.
FORMULA
Inverse binomial transform of A051185.
EXAMPLE
The a(3) = 27 spanning intersecting set-systems:
{{1,2,3}}
{{1},{1,2,3}}
{{2},{1,2,3}}
{{3},{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,2},{1,2,3}}
{{1,3},{2,3}}
{{1,3},{1,2,3}}
{{2,3},{1,2,3}}
{{1},{1,2},{1,3}}
{{1},{1,2},{1,2,3}}
{{1},{1,3},{1,2,3}}
{{2},{1,2},{2,3}}
{{2},{1,2},{1,2,3}}
{{2},{2,3},{1,2,3}}
{{3},{1,3},{2,3}}
{{3},{1,3},{1,2,3}}
{{3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,2},{1,3},{1,2,3}}
{{1,2},{2,3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{1},{1,2},{1,3},{1,2,3}}
{{2},{1,2},{2,3},{1,2,3}}
{{3},{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}
MATHEMATICA
Length/@Table[Select[Subsets[Rest[Subsets[Range[n]]]], And[Union@@#==Range[n], FreeQ[Intersection@@@Tuples[#, 2], {}]]&], {n, 1, 4}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 11 2018
STATUS
approved