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 A060579 Number of homeomorphically irreducible general graphs on 4 labeled nodes and with n edges. 0
 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; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2. REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983. LINKS FORMULA 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!. CROSSREFS Cf. A003514, A060516, A060533-A060537, A060576-A060581. Sequence in context: A055916 A266472 A259804 * A183326 A123950 A100191 Adjacent sequences:  A060576 A060577 A060578 * A060580 A060581 A060582 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Apr 03 2001 STATUS approved

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Last modified December 13 01:23 EST 2019. Contains 329963 sequences. (Running on oeis4.)