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Number of locally disjoint rooted trees with n nodes, meaning no branch overlaps any other (unequal) branch of the same root.
29

%I #11 Jun 20 2020 03:20:28

%S 1,1,2,4,9,19,44,99,233,554,1346,3300,8219,20635,52300,133488,343033,

%T 886360,2302133,6005835

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

%H Gus Wiseman, <a href="/A316473/a316473.png">The a(6) = 19 locally disjoint rooted trees.</a>

%e The a(5) = 9 locally disjoint rooted trees:

%e ((((o))))

%e (((oo)))

%e ((o(o)))

%e ((ooo))

%e (o((o)))

%e (o(oo))

%e ((o)(o))

%e (oo(o))

%e (oooo)

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

%t Table[Length[strut[n]],{n,15}]

%Y Cf. A000081, A285573, A302696, A304713, A316468, A316470, A316471, A316475, A316495.

%K nonn,more

%O 1,3

%A _Gus Wiseman_, Jul 04 2018

%E a(20) from _Jinyuan Wang_, Jun 20 2020