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A306844
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Number of anti-transitive rooted trees with n nodes.
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40
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1, 1, 2, 3, 7, 14, 36, 83, 212, 532, 1379, 3577, 9444, 25019, 66943, 179994, 487031, 1323706, 3614622, 9907911
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OFFSET
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1,3
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COMMENTS
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A rooted tree is anti-transitive if the subbranches are disjoint from the branches, i.e., no branch of a branch is a branch.
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LINKS
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Table of n, a(n) for n=1..20.
Gus Wiseman, The a(7) = 36 anti-transitive rooted trees.
Gus Wiseman, The a(10) = 532 anti-transitive rooted trees.
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EXAMPLE
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The a(1) = 1 through a(6) = 14 anti-transitive rooted trees:
o (o) (oo) (ooo) (oooo) (ooooo)
((o)) ((oo)) ((ooo)) ((oooo))
(((o))) (((oo))) (((ooo)))
((o)(o)) ((o)(oo))
((o(o))) ((o(oo)))
(o((o))) ((oo(o)))
((((o)))) (o((oo)))
(oo((o)))
((((oo))))
(((o)(o)))
(((o(o))))
((o((o))))
(o(((o))))
(((((o)))))
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MATHEMATICA
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rtall[n_]:=Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])];
Table[Length[Select[rtall[n], Intersection[Union@@#, #]=={}&]], {n, 10}]
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CROSSREFS
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Cf. A276625, A279861, A279861, A290689, A290760, A304360.
Cf. A324694, A324695, A324738, A324741, A324743, A324751, A324754, A324756, A324758, A324759, A324764.
Sequence in context: A191491 A210345 A006660 * A213906 A123777 A245899
Adjacent sequences: A306841 A306842 A306843 * A306845 A306846 A306847
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KEYWORD
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nonn,more
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AUTHOR
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Gus Wiseman, Mar 13 2019
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EXTENSIONS
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a(16)-a(20) from Jinyuan Wang, Jun 20 2020
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STATUS
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approved
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