A052113 Number of self-complementary directed 2-multigraphs with loops on n nodes.

1, 5, 41, 1023, 67173, 10771355, 5957216417, 6971880064072, 32181855124938673, 290910256437910060602, 11266525980714327353251353, 815201852317091835592374861144, 266236010885685869904935495261864265, 157899403462038839125137738939159318226008

Offset: 1

Author

Vladeta Jovovic, Jan 21 2000

Keywords

• nonn

Comments

A 2-multigraph is similar to an ordinary graph except there are 0, 1 or 2 edges between any two nodes (self-loops are not allowed).

References

• V. Jovovic, On the number of m-place relations (in Russian), Logiko-algebraicheskie konstruktsii, Tver, 1992, 59-66.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A004105, A047832.

Programs

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) = {2*sum(i=2, #v, sum(j=1, i-1, if(v[i]*v[j]%2==0, gcd(v[i],v[j])))) + sum(i=1, #v, if(v[i]%2==0, v[i]))}
a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^edges(p)); s/n!} \\ Andrew Howroyd, Sep 16 2018

Extensions

Terms a(14) and beyond from Andrew Howroyd, Sep 16 2018