cp's OEIS Frontend

A319719 Number of non-isomorphic connected antichains of multisets of weight n.

%I A319719 #5 Sep 26 2018 16:26:36
%S A319719 1,1,3,4,10,14,48,95,305,822,2615
%N A319719 Number of non-isomorphic connected antichains of multisets of weight n.
%C A319719 In an antichain, no part is a proper submultiset of any other. The weight of an antichain is the sum of sizes of its parts. Weight is generally not the same as number of vertices. Connected antichains are also called clutters.
%H A319719 Goran Kilibarda and Vladeta Jovovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Kilibarda/kili2.pdf">Antichains of Multisets</a>, Journal of Integer Sequences, Vol. 7 (2004).
%e A319719 Non-isomorphic representatives of the a(1) = 1 through a(4) = 10 connected antichains:
%e A319719 1: {{1}}
%e A319719 2: {{1,1}}
%e A319719    {{1,2}}
%e A319719    {{1},{1}}
%e A319719 3: {{1,1,1}}
%e A319719    {{1,2,2}}
%e A319719    {{1,2,3}}
%e A319719    {{1},{1},{1}}
%e A319719 4: {{1,1,1,1}}
%e A319719    {{1,1,2,2}}
%e A319719    {{1,2,2,2}}
%e A319719    {{1,2,3,3}}
%e A319719    {{1,2,3,4}}
%e A319719    {{1,1},{1,1}}
%e A319719    {{1,2},{1,2}}
%e A319719    {{1,2},{2,2}}
%e A319719    {{1,3},{2,3}}
%e A319719    {{1},{1},{1},{1}}
%Y A319719 Cf. A001055, A001970, A007716, A007718, A056156, A096827, A253249, A285573, A293994, A318099, A319557, A319616-A319646, A319721.
%K A319719 nonn,more
%O A319719 0,3
%A A319719 _Gus Wiseman_, Sep 26 2018