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A060533
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Number of homeomorphically irreducible multigraphs (or series-reduced multigraphs or multigraphs without nodes of degree 2) on 3 labeled nodes.
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11
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1, 3, 0, 3, 9, 12, 19, 27, 36, 46, 57, 69, 82, 96, 111, 127, 144, 162, 181, 201, 222, 244, 267, 291, 316, 342, 369, 397, 426, 456, 487, 519, 552, 586, 621, 657, 694, 732, 771, 811, 852
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
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LINKS
| Vladeta Jovovic, Generating functions for homeomorphically irreducible multigraphs on n labeled nodes
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FORMULA
| G.f.: (3*x^7 - 7*x^6 + 6*x^5 + 3*x^4 - 11*x^3 + 6*x^2 - 1)/(x - 1)^3. E.g.f. for homeomorphically irreducible multigraphs with n nodes and k edges is (1 + x*y)^( - 1/2)*exp(x*y/2 + x^2*y^2/4)*Sum_{k >= 0} 1/(1 - x)^binomial(k, 2)*exp( - x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.
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MATHEMATICA
| i=5; s=1; lst={s}; Do[s+=n+i; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 30 2008]
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CROSSREFS
| Cf. A003514, A060516, A060534-A060537.
Sequence in context: A117078 A021333 A104141 * A177785 A191619 A157525
Adjacent sequences: A060530 A060531 A060532 * A060534 A060535 A060536
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 01 2001
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