A304887 Number of non-isomorphic blobs of weight n.

1, 1, 1, 1, 1, 1, 3, 3, 8, 14

Offset

0,7

Comments

A blob is a connected antichain of finite sets that cannot be capped by a hypertree with more than one branch. The weight of a blob is the sum of cardinalities of its elements. Weight is generally not the same as number of vertices (see A275307).

Links

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

Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.

Example

Non-isomorphic representatives of the a(8) = 8 blobs are the following:
  {{1,2,3,4,5,6,7,8}}
  {{1,5,6},{2,3,4,5,6}}
  {{1,2,5,6},{3,4,5,6}}
  {{1,3,4,5},{2,3,4,5}}
  {{1,2},{1,3,4},{2,3,4}}
  {{1,4},{1,5},{2,3,4,5}}
  {{2,4},{1,2,5},{3,4,5}}
  {{1,2},{1,3},{2,4},{3,4}}

Crossrefs

Cf. A030019, A035053, A048143, A275307, A283877, A286520, A293607, A293993, A293994, A304118, A304867.

Sequence in context: A303902 A090597 A369084 * A126073 A126592 A055057

Adjacent sequences: A304884 A304885 A304886 * A304888 A304889 A304890

Keyword

nonn,more

Author

Gus Wiseman, May 20 2018

Status

approved