A014396 Number of loopless multigraphs with 6 nodes and n edges.

1, 1, 3, 8, 21, 52, 132, 313, 741, 1684, 3711, 7895, 16310, 32604, 63363, 119745, 220546, 396428, 696750, 1198812, 2022503, 3349574, 5452496, 8732932, 13776366, 21423968, 32872642, 49804323, 74560913, 110369469, 161639227

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• CRC Handbook of Combinatorial Designs, 1996, p. 650.
• F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 88, (4.1.18).
• J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 517.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Crossrefs

Row 6 of A192517.

Cf. A001399, A003082, A014395, A014397, A014398.

Programs

Mathematica

CoefficientList[Series[PairGroupIndex[SymmetricGroup[6],s]/.Table[s[i]->1/(1-x^i),{i,1,Binomial[6,2]}],{x,0,30}],x] (* Geoffrey Critzer, Oct 14 2012 *)

PARI

concat([1], G(6, 40)) \\ See A191646 for G. - Andrew Howroyd, Mar 15 2020

Extensions

More terms and better description from Vladeta Jovovic, Dec 29 1999