A316471 - OEIS

%I #6 Jul 05 2018 02:30:18

%S 1,1,1,2,3,6,11,21,43,89,185,391,840,1822,3975,8727,19280,42841,95661,

%T 214490

%N Number of locally disjoint rooted identity trees with n nodes, meaning no branch overlaps any other branch of the same root.

%H Gus Wiseman, <a href="/A316471/a316471.png">The a(8) = 21 locally disjoint rooted identity trees.</a>

%e The a(7) = 11 locally disjoint rooted identity trees:

%e ((((((o))))))

%e ((((o(o)))))

%e (((o((o)))))

%e ((o(((o)))))

%e ((o(o(o))))

%e (((o)((o))))

%e (o((((o)))))

%e (o((o(o))))

%e (o(o((o))))

%e ((o)(((o))))

%e (o(o)((o)))

%t strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],UnsameQ@@#&&Select[Tuples[#,2],UnsameQ@@#&&(Intersection@@#=!={})&]=={}&]];

%t Table[Length[strut[n]],{n,20}]

%Y Cf. A000081, A004111, A276625, A277098, A302696, A303362, A304713, A316467, A316471, A316473, A316474, A316494.

%K nonn,more

%O 1,4

%A _Gus Wiseman_, Jul 04 2018