A261174 Number of multigraphs on 4 unlabeled nodes with n edges where the edges can be of two colors.

1, 2, 9, 30, 90, 248, 650, 1560, 3560, 7680, 15786, 31076, 58905, 107768, 191180, 329664, 554038, 909558, 1461655, 2302950, 3563482, 5422392, 8124040, 11997648, 17482295, 25156872, 35779092, 50330364, 70072640, 96615760, 131999058, 178786960, 240186182, 320179470

Offset

0,2

Links

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

Formula

G.f.: (1 - 2*x + 5*x^2 + 2*x^3 + 10*x^4 + 12*x^5 + 32*x^6 + 20*x^7 + 56*x^8 + 20*x^9 + 32*x^10 + 12*x^11 + 10*x^12 + 2*x^13 + 5*x^14 - 2*x^15 + x^16)/((1 - x)^12*(1 + x)^4*(1 + x^2)^2*(1 + x + x^2)^4). - Andrew Howroyd, Apr 18 2021

Mathematica

Needs["Combinatorica`"]; n = 4; nn = 25; CoefficientList[Series[PairGroupIndex[SymmetricGroup[n], s] /.Table[s[i] -> 1/(1 - x^i)^2, {i, 1, Binomial[n, 2]}], {x, 0, nn}], x]

Prog

(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^g )) * prod(i=1, #v, my(c=v[i]); t(c)^((c-1)\2)*if(c%2, 1, t(c/2)))}
G(n)={my(s=0); forpart(p=n, s+=permcount(p)/edges(p, i->(1-x^i)^2)); s/n!}
{ Vec(G(4) + O(x^36)) } \\ Andrew Howroyd, Apr 18 2021

Crossrefs

Cf. A050531 (case of 3 nodes).

Sequence in context: A290746 A268586 A056288 * A273652 A056283 A192518

Adjacent sequences: A261171 A261172 A261173 * A261175 A261176 A261177

Keyword

nonn

Author

Geoffrey Critzer, Aug 10 2015

Extensions

Terms a(26) and beyond from Andrew Howroyd, Apr 18 2021

Status

approved