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Search: id:A138387
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| A138387 |
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Numbers of unlabeled graphs with n vertices and 2 unicyclic components. |
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+0
2
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| 1, 2, 8, 23, 74, 220, 674, 2011, 6038, 17980, 53547, 158907, 471225, 1394786, 4124929, 12185636, 35972082, 106111713, 312835608, 921809509, 2715058701, 7993741597, 23527694230, 69228383367, 203648980297, 598945442071
(list; graph; listen)
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OFFSET
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6,2
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COMMENT
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This sequence is the second row of table T of A137918.
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FORMULA
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For n odd, a(n) = Sum(3 <= i <= (n-1)/2){f(i) * f(n-i)}; for n even, a(n) = Sum(3 <= i <= n/2 - 1){f(i) * f(n-i)} + (f(n/2)+1)*f(n/2)/2, where f(k) is A001429(k).
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EXAMPLE
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a(13) = 2,011, since n is odd and the partitions are 3+10, 4+9, 5+8 and 6+7. This gives 657 + 480 + 445 + 429 graphs.
Note that f(4)= 2, f(5) = 5, f(6) = 13, f(7) = 33, f(8) = 89, f(9) = 240 and f(10) = 657.
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CROSSREFS
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Cf. A001429, A137918.
Sequence in context: A154144 A018042 A072842 this_sequence A007346 A062247 A084744
Adjacent sequences: A138384 A138385 A138386 this_sequence A138388 A138389 A138390
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KEYWORD
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easy,nonn
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AUTHOR
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Washington G. Bomfim (webonfim(AT)bol.com.br), Mar 18 2008
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