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A318185
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Number of totally transitive rooted trees with n nodes.
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23
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1, 1, 1, 2, 3, 5, 7, 12, 17, 28, 41, 65, 96, 150, 221, 342, 506, 771, 1142, 1731, 2561, 3855, 5702, 8538, 12620, 18817, 27774, 41276, 60850, 90139
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OFFSET
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1,4
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The a(8) = 12 totally transitive rooted trees:
(o(o)(o(o)))
(o(o)(o)(o))
(o(o)(ooo))
(o(oo)(oo))
(oo(o)(oo))
(ooo(o)(o))
(o(ooooo))
(oo(oooo))
(ooo(ooo))
(oooo(oo))
(ooooo(o))
(ooooooo)
The a(9) = 17 totally transitive rooted trees:
(o(o)(oo(o)))
(oo(o)(o(o)))
(o(o)(o)(oo))
(oo(o)(o)(o))
(o(o)(oooo))
(o(oo)(ooo))
(oo(o)(ooo))
(oo(oo)(oo))
(ooo(o)(oo))
(oooo(o)(o))
(o(oooooo))
(oo(ooooo))
(ooo(oooo))
(oooo(ooo))
(ooooo(oo))
(oooooo(o))
(oooooooo)
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MATHEMATICA
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totra[n_]:=totra[n]=If[n==1, {{}}, Join@@Table[Select[Union[Sort/@Tuples[totra/@c]], Complement[Union@@#, #]=={}&], {c, IntegerPartitions[n-1]}]];
Table[Length[totra[n]], {n, 20}]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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