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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
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
Sequence in context: A007056 A026551 A296719 * A147078 A341704 A146416
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.)