A327335 - OEIS

%I #4 Sep 02 2019 08:05:45

%S 0,1,4,18,216

%N Number of non-isomorphic set-systems with n vertices and at least one endpoint/leaf.

%C A set-system is a finite set of finite nonempty sets. Elements of a set-system are sometimes called edges. A leaf is an edge containing a vertex that does not belong to any other edge, while an endpoint is a vertex belonging to only one edge.

%C Also covering set-systems with minimum covered vertex-degree 1.

%e Non-isomorphic representatives of the a(1) = 1 through a(3) = 18 set-systems:

%e   {{1}}  {{1}}        {{1}}

%e          {{1,2}}      {{1,2}}

%e          {{1},{2}}    {{1},{2}}

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

%e                       {{1},{1,2}}

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

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

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

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

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

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

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

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

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

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

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

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

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

%Y Unlabeled set-systems are A000612.

%Y The labeled version is A327228.

%Y The covering version is A327230 (first differences).

%Y Cf. A002494, A245797, A261919, A283877, A327103, A327105, A327197, A327227, A327229, A327336.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Sep 02 2019