cp's OEIS Frontend

A318185 Number of totally transitive rooted trees with n nodes.

%I A318185 #5 Aug 22 2018 08:32:56
%S A318185 1,1,1,2,3,5,7,12,17,28,41,65,96,150,221,342,506,771,1142,1731,2561,
%T A318185 3855,5702,8538,12620,18817,27774,41276,60850,90139
%N A318185 Number of totally transitive rooted trees with n nodes.
%C A318185 A rooted tree is totally transitive if every branch of the root is totally transitive and every branch of a branch of the root is also a branch of the root. Unlike transitive rooted trees (A290689), every terminal subtree of a totally transitive rooted tree is itself totally transitive.
%e A318185 The a(8) = 12 totally transitive rooted trees:
%e A318185   (o(o)(o(o)))
%e A318185   (o(o)(o)(o))
%e A318185   (o(o)(ooo))
%e A318185   (o(oo)(oo))
%e A318185   (oo(o)(oo))
%e A318185   (ooo(o)(o))
%e A318185   (o(ooooo))
%e A318185   (oo(oooo))
%e A318185   (ooo(ooo))
%e A318185   (oooo(oo))
%e A318185   (ooooo(o))
%e A318185   (ooooooo)
%e A318185 The a(9) = 17 totally transitive rooted trees:
%e A318185   (o(o)(oo(o)))
%e A318185   (oo(o)(o(o)))
%e A318185   (o(o)(o)(oo))
%e A318185   (oo(o)(o)(o))
%e A318185   (o(o)(oooo))
%e A318185   (o(oo)(ooo))
%e A318185   (oo(o)(ooo))
%e A318185   (oo(oo)(oo))
%e A318185   (ooo(o)(oo))
%e A318185   (oooo(o)(o))
%e A318185   (o(oooooo))
%e A318185   (oo(ooooo))
%e A318185   (ooo(oooo))
%e A318185   (oooo(ooo))
%e A318185   (ooooo(oo))
%e A318185   (oooooo(o))
%e A318185   (oooooooo)
%t A318185 totra[n_]:=totra[n]=If[n==1,{{}},Join@@Table[Select[Union[Sort/@Tuples[totra/@c]],Complement[Union@@#,#]=={}&],{c,IntegerPartitions[n-1]}]];
%t A318185 Table[Length[totra[n]],{n,20}]
%Y A318185 Cf. A000081, A001678, A004111, A279861, A290689, A290760, A290822, A318186, A318187.
%K A318185 nonn,more
%O A318185 1,4
%A A318185 _Gus Wiseman_, Aug 20 2018