A304887 - OEIS

%I #5 May 21 2018 03:26:20

%S 1,1,1,1,1,1,3,3,8,14

%N Number of non-isomorphic blobs of weight n.

%C 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).

%H Gus Wiseman, <a href="http://www.mathematica-journal.com/2017/12/every-clutter-is-a-tree-of-blobs/">Every Clutter Is a Tree of Blobs</a>, The Mathematica Journal, Vol. 19, 2017.

%e Non-isomorphic representatives of the a(8) = 8 blobs are the following:

%e   {{1,2,3,4,5,6,7,8}}

%e   {{1,5,6},{2,3,4,5,6}}

%e   {{1,2,5,6},{3,4,5,6}}

%e   {{1,3,4,5},{2,3,4,5}}

%e   {{1,2},{1,3,4},{2,3,4}}

%e   {{1,4},{1,5},{2,3,4,5}}

%e   {{2,4},{1,2,5},{3,4,5}}

%e   {{1,2},{1,3},{2,4},{3,4}}

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

%K nonn,more

%O 0,7

%A _Gus Wiseman_, May 20 2018