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1, 1, 2, 4, 7, 14, 27, 56, 116, 253, 557, 1272, 2948, 6998, 16856, 41306, 102449, 257294, 652566, 1670679, 4311109, 11206278, 29316294, 77144518, 204072054, 542446974, 1448230644, 3882179984, 10445521740, 28202158173, 76387639678
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) is the number of forests with n unlabeled nodes without trees of order 2. This follows from the fact that for n>=2 A005195(n-2) counts the forests of order n with one or more trees of order 2.
The unique forest of order 1 is an isolated vertex, so a(1)=1. For n>=2, a(n) - a(n-1) counts forests of order n with trees of order >=3.
A005195(n) - A005195(n-3) counts forests of order n without trees of order 3.
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EXAMPLE
| a(5) = 7 since the only options are: 3 trees of order 5; 2 forests composed by trees of orders 4 and l; one forest with trees of orders [3 1 1]; and one forest with five isolated nodes.
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CROSSREFS
| Cf. A005195, A000055(trees).
Sequence in context: A171231 A094057 A119267 * A018254 A018660 A018692
Adjacent sequences: A144975 A144976 A144977 * A144979 A144980 A144981
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KEYWORD
| nonn
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AUTHOR
| W. Bomfim (webonfim(AT)bol.com.br), Sep 28 2008
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