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A331488
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Number of unlabeled lone-child-avoiding rooted trees with n vertices and more than two branches (of the root).
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9
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0, 0, 0, 1, 1, 2, 3, 6, 10, 20, 36, 70, 134, 263, 513, 1022, 2030, 4076, 8203, 16614, 33738, 68833, 140796, 288989, 594621, 1226781, 2536532, 5256303, 10913196, 22700682, 47299699, 98714362, 206323140, 431847121, 905074333, 1899247187, 3990145833, 8392281473
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OFFSET
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1,6
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COMMENTS
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Also the number of lone-child-avoiding rooted trees with n vertices and more than two branches.
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LINKS
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FORMULA
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EXAMPLE
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The a(4) = 1 through a(9) = 10 trees:
(ooo) (oooo) (ooooo) (oooooo) (ooooooo) (oooooooo)
(oo(oo)) (oo(ooo)) (oo(oooo)) (oo(ooooo))
(ooo(oo)) (ooo(ooo)) (ooo(oooo))
(oooo(oo)) (oooo(ooo))
(o(oo)(oo)) (ooooo(oo))
(oo(o(oo))) (o(oo)(ooo))
(oo(o(ooo)))
(oo(oo)(oo))
(oo(oo(oo)))
(ooo(o(oo)))
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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], Length[#]>2&&FreeQ[#, {_}]&]], {n, 10}]
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CROSSREFS
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The not necessarily lone-child-avoiding version is A331233.
The Matula-Goebel numbers of these trees are listed by A331490.
A000081 counts unlabeled rooted trees.
A001678 counts lone-child-avoiding rooted trees.
A001679 counts topologically series-reduced rooted trees.
A291636 lists Matula-Goebel numbers of lone-child-avoiding rooted trees.
A331489 lists Matula-Goebel numbers of series-reduced rooted trees.
Cf. A000014, A000669, A004250, A007097, A007821, A033942, A060313, A060356, A061775, A109082, A109129, A196050, A276625, A330943.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Terminology corrected (lone-child-avoiding, not series-reduced) by Gus Wiseman, May 10 2021
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STATUS
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approved
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