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A305843 Number of labeled spanning intersecting set-systems on n vertices. 34
1, 1, 3, 27, 1245, 1308285, 912811093455, 291201248260060977862887, 14704022144627161780742038728709819246535634969, 12553242487940503914363982718112298267975272588471811456164576678961759219689708372356843289 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..9.

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

Cf. A001206, A006126, A048143, A051185, A134958, A030019, A304985, A305844.

Sequence in context: A279832 A012012 A229866 * A192341 A191511 A102580

Adjacent sequences:  A305840 A305841 A305842 * A305844 A305845 A305846

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 11 2018

STATUS

approved

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Last modified March 31 16:23 EDT 2020. Contains 333151 sequences. (Running on oeis4.)