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Search: id:A060579
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| A060579 |
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Number of homeomorphically irreducible general graphs on 4 labeled nodes and with n edges. |
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+0
1
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| 1, 6, 19, 68, 242, 704, 1981, 5140, 12364, 27614, 57598, 113108, 210812, 375606, 643646, 1066196, 1714445, 2685464, 4109493, 6158768, 9058119, 13097592, 18647371, 26175300, 36267330, 49651242, 67224024, 90083308, 119563302
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2.
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
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LINKS
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V. Jovovic, Generating functions for homeomorphically irreducible general graphs on n labeled nodes
V. Jovovic, Recurrences for the numbers of homeomorphically irreducible general graphs on m labeled nodes and n edges
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FORMULA
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G.f.: (4*x^15 + 5*x^14 - 194*x^13 + 881*x^12 - 2058*x^11 + 3096*x^10 - 3330*x^9 + 2628*x^8 - 1398*x^7 + 359*x^6 + 72*x^5 - 93*x^4 + 28*x^3 + 4*x^2 - 4*x + 1)/(x - 1)^10. E.g.f. for homeomorphically irreducible general graphs 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 + 1, 2)*exp( - x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.
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CROSSREFS
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Cf. A003514, A060516, A060533-A060537, A060576-A060581.
Adjacent sequences: A060576 A060577 A060578 this_sequence A060580 A060581 A060582
Sequence in context: A041673 A137195 A055916 this_sequence A100191 A123950 A026545
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 03 2001
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