The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Cf. A003514, A060516, A060533-A060537, A060576-A060581. Sequence in context: A007056 A026551 A296719 * A147078 A146416 A260185 Adjacent sequences:  A060575 A060576 A060577 * A060579 A060580 A060581 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Apr 03 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 30 11:55 EDT 2020. Contains 337439 sequences. (Running on oeis4.)