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A316474
Number of locally stable rooted identity trees with n nodes, meaning no branch is a subset of any other branch of the same root.
9
1, 1, 1, 1, 1, 2, 3, 5, 8, 14, 23, 42, 73, 133, 241, 442, 812, 1508, 2802, 5247, 9842, 18554, 35045, 66453, 126249
OFFSET
1,6
EXAMPLE
The a(9) = 8 locally stable rooted identity trees:
((((((((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@@#&&Complement@@#=={}&]=={}&]];
Table[Length[strut[n]], {n, 20}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 04 2018
STATUS
approved