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Search: id:A144977
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| 1, 1, 3, 7, 16, 41, 108, 301, 881, 2684, 8455, 27444, 91248, 309593, 1068584, 3742171, 13269281, 47561455, 172092274, 627887239, 2307902495, 8539497952, 31786480760, 118960956585, 447413177185, 1690336204778, 6412656031161
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) is the number of hyperforests with n unlabeled nodes without trees of order 2. This follows from the fact that for n>=2 A134955(n-2) counts the hyperforests of order n with one or more trees of order 2.
The unique hyperforest (without loops) of order 1 is an isolated vertex, so a(1) = 1.
For n>=2, a(n) - a(n-1) counts hyperforests of order n with components of order >=3.
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EXAMPLE
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a(3) = 3 since the only options are 2 hypertrees of order 3, or the forest composed by 3 isolated nodes.
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CROSSREFS
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Cf. A134955, A035053(hypertrees).
Sequence in context: A009337 A036567 A018023 this_sequence A058300 A000674 A129045
Adjacent sequences: A144974 A144975 A144976 this_sequence A144978 A144979 A144980
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KEYWORD
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nonn
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AUTHOR
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W. Bomfim (webonfim(AT)bol.com.br), Sep 28 2008
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