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A317718
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Number of uniform relatively prime rooted trees with n nodes.
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11
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1, 1, 2, 4, 7, 13, 27, 55, 125, 278, 650, 1510, 3624, 8655, 21017, 51212, 125857, 310581, 770767, 1920226
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OFFSET
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1,3
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COMMENTS
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An unlabeled rooted tree is uniform and relatively prime iff either it is a single node or a single node with a single uniform relatively prime branch, or the branches of the root have empty intersection (relatively prime) and equal multiplicities (uniform) and are themselves uniform relatively prime trees.
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LINKS
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Table of n, a(n) for n=1..20.
A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp. 1-12.
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EXAMPLE
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The a(6) = 13 uniform relatively prime rooted trees:
(((((o)))))
((((oo))))
(((o(o))))
(((ooo)))
((o((o))))
((o(oo)))
((oooo))
(o(((o))))
(o((oo)))
(o(o(o)))
(o(ooo))
((o)((o)))
(ooooo)
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MATHEMATICA
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purt[n_]:=purt[n]=If[n==1, {{}}, Join@@Table[Select[Union[Sort/@Tuples[purt/@ptn]], Or[Length[#]==1, And[SameQ@@Length/@Split[#], Intersection@@#=={}]]&], {ptn, IntegerPartitions[n-1]}]];
Table[Length[purt[n]], {n, 20}]
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CROSSREFS
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Cf. A000081, A001190, A004111, A072774, A301700, A317588.
Cf. A317705, A317707, A317708, A317709, A317710, A317711, A317712, A317717.
Sequence in context: A309050 A265580 A136408 * A103104 A103480 A024826
Adjacent sequences: A317715 A317716 A317717 * A317719 A317720 A317721
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KEYWORD
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nonn,more
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AUTHOR
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Gus Wiseman, Aug 05 2018
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STATUS
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approved
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