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

0,3

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

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)).

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 *)

Prog

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

Crossrefs

Row 5 of A192517.

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

Sequence in context: A034482 A114100 A260677 * A326520 A295146 A014314

Adjacent sequences: A014392 A014393 A014394 * A014396 A014397 A014398

Keyword

easy,nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Dec 23 1999

Status

approved