A014395 Number of multigraphs with 5 nodes and n edges.

1, 1, 3, 7, 17, 35, 76, 149, 291, 539, 974, 1691, 2874, 4730, 7620, 11986, 18485, 27944, 41550, 60744, 87527, 124338, 174403, 241650, 331153, 448987, 602853, 801943, 1057615, 1383343, 1795578, 2313595, 2960656, 3763879, 4755505, 5972927, 7460196, 9267980

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• 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 5 of A192517.

Cf. A001399, A003082, A014396, A014397, A014398.

Programs

Mathematica

CoefficientList[Series[PairGroupIndex[SymmetricGroup[5],s]/.Table[s[i]->1/(1-x^i),{i,1,Binomial[5,2]}],{x,0,30}],x] (* Geoffrey Critzer, Oct 14 2012 *)

PARI

concat([1], G(5, 40)) \\ See A191646 for G. - Andrew Howroyd, Mar 15 2020

Formula

G.f.: (x^21 + x^20 + 5*x^19 + 8*x^18 + 14*x^17 + 22*x^16 + 32*x^15 + 40*x^14 + 39*x^13 + 47*x^12 + 36*x^11 + 36*x^10 + 25*x^9 + 21*x^8 + 12*x^7 + 11*x^6 + 4*x^5 + 4*x^4 + x^3 + x^2 - x + 1)/((x^6 - 1)*(x^5 - 1)^2*(x^4 - 1)^2*(x^3 - 1)^2*(x - 1)^3*(x + 1)).

Extensions

More terms from Vladeta Jovovic, Dec 23 1999