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A325697
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Number of rooted trees with n vertices with no proper terminal subtree appearing at only one position.
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0
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1, 0, 1, 1, 2, 2, 5, 5, 11, 13, 27, 30, 69, 76, 168
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OFFSET
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1,5
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COMMENTS
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The Matula-Goebel numbers of these trees are given by A325661.
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LINKS
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EXAMPLE
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The a(4) = 1 through a(9) = 11 rooted trees:
(ooo) (oooo) (ooooo) (oooooo) (ooooooo) (oooooooo)
((o)(o)) (o(o)(o)) ((oo)(oo)) (o(oo)(oo)) ((ooo)(ooo))
(oo(o)(o)) (ooo(o)(o)) (oo(oo)(oo))
((o)(o)(o)) (o(o)(o)(o)) (oooo(o)(o))
(((o))((o))) (o((o))((o))) (oo(o)(o)(o))
(((oo))((oo)))
((o)(o)(o)(o))
((o(o))(o(o)))
(oo((o))((o)))
((o)((o))((o)))
((((o)))(((o))))
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MATHEMATICA
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urt[n_]:=Join@@Table[Union[Sort/@Tuples[urt/@ptn]], {ptn, IntegerPartitions[n-1]}];
Table[Length[Select[urt[n], !MemberQ[Length/@Split[Sort[Extract[#, Most[Position[#, _List]]]]], 1]&]], {n, 15}]
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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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