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A316471
Number of locally disjoint rooted identity trees with n nodes, meaning no branch overlaps any other branch of the same root.
21
1, 1, 1, 2, 3, 6, 11, 21, 43, 89, 185, 391, 840, 1822, 3975, 8727, 19280, 42841, 95661, 214490
OFFSET
1,4
EXAMPLE
The a(7) = 11 locally disjoint rooted identity trees:
((((((o))))))
((((o(o)))))
(((o((o)))))
((o(((o)))))
((o(o(o))))
(((o)((o))))
(o((((o)))))
(o((o(o))))
(o(o((o))))
((o)(((o))))
(o(o)((o)))
MATHEMATICA
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@@#=!={})&]=={}&]];
Table[Length[strut[n]], {n, 20}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 04 2018
STATUS
approved