login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323293 Number of 3-uniform hypergraphs on n labeled vertices where no two edges have two vertices in common. 6
1, 1, 1, 2, 5, 26, 271, 5596, 231577, 21286940 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

EXAMPLE

The a(5) = 26 hypergraphs:

  {}

  {{1,2,3}}

  {{1,2,4}}

  {{1,2,5}}

  {{1,3,4}}

  {{1,3,5}}

  {{1,4,5}}

  {{2,3,4}}

  {{2,3,5}}

  {{2,4,5}}

  {{3,4,5}}

  {{1,2,3},{1,4,5}}

  {{1,2,3},{2,4,5}}

  {{1,2,3},{3,4,5}}

  {{1,2,4},{1,3,5}}

  {{1,2,4},{2,3,5}}

  {{1,2,4},{3,4,5}}

  {{1,2,5},{1,3,4}}

  {{1,2,5},{2,3,4}}

  {{1,2,5},{3,4,5}}

  {{1,3,4},{2,3,5}}

  {{1,3,4},{2,4,5}}

  {{1,3,5},{2,3,4}}

  {{1,3,5},{2,4,5}}

  {{1,4,5},{2,3,4}}

  {{1,4,5},{2,3,5}}

Non-isomorphic representatives of the 6 unlabeled 3-uniform hypertrees spanning 6 vertices where no two edges have two vertices in common, and their multiplicities in the labeled case which add up to a(6) = 271:

    1 X {}

   20 X {{1,2,3}}

   90 X {{1,2,5},{3,4,5}}

   10 X {{1,2,3},{4,5,6}}

  120 X {{1,3,5},{2,3,6},{4,5,6}}

   30 X {{1,2,4},{1,3,5},{2,3,6},{4,5,6}}

MATHEMATICA

stableSets[u_, Q_]:=If[Length[u]===0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r===w||Q[r, w]||Q[w, r]], Q]]]];

Table[Length[stableSets[Subsets[Range[n], {3}], Length[Intersection[#1, #2]]>1&]], {n, 8}]

CROSSREFS

Cf. A000665, A025035, A125791, A190865, A289837, A302374, A302394, A319540, A320395, A322451, A323292-A323299.

Sequence in context: A180749 A323299 A111195 * A258868 A322705 A167007

Adjacent sequences:  A323290 A323291 A323292 * A323294 A323295 A323296

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jan 10 2019

EXTENSIONS

a(9) from Andrew Howroyd, Aug 14 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 16:44 EDT 2020. Contains 334626 sequences. (Running on oeis4.)