VOOZH about

URL: https://oeis.org/A261174

⇱ A261174 - OEIS

login
A261174
Number of multigraphs on 4 unlabeled nodes with n edges where the edges can be of two colors.
1
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
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
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Aug 10 2015
EXTENSIONS
Terms a(26) and beyond from Andrew Howroyd, Apr 18 2021
STATUS
approved