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 A060578 Number of homeomorphically irreducible general graphs on 3 labeled node and with n edges. 0
 1, 3, 9, 21, 60, 135, 282, 537, 945, 1561, 2451, 3693, 5378, 7611, 10512, 14217, 18879, 24669, 31777, 40413, 50808, 63215, 77910, 95193, 115389, 138849, 165951, 197101, 232734, 273315, 319340, 371337, 429867, 495525, 568941, 650781, 741748 (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 Table of n, a(n) for n=0..36. 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 FORMULA G.f.: - (8*x^9 - 36*x^8 + 66*x^7 - 70*x^6 + 51*x^5 - 24*x^4 + 8*x^3 - 6*x^2 + 3*x - 1)/(x - 1)^6. 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!. MATHEMATICA CoefficientList[Series[-(8x^9-36x^8+66x^7-70x^6+51x^5-24x^4+8x^3-6x^2+3x-1)/(x-1)^6, {x, 0, 40}], x] (* Harvey P. Dale, Jul 22 2018 *) CROSSREFS Cf. A003514, A060516, A060533-A060537, A060576-A060581. Sequence in context: A007056 A026551 A296719 * A147078 A341704 A146416 Adjacent sequences: A060575 A060576 A060577 * A060579 A060580 A060581 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Apr 03 2001 STATUS approved

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Last modified March 1 08:46 EST 2024. Contains 370430 sequences. (Running on oeis4.)