A052113 - OEIS

%I #8 Sep 16 2018 16:51:17

%S 1,5,41,1023,67173,10771355,5957216417,6971880064072,

%T 32181855124938673,290910256437910060602,11266525980714327353251353,

%U 815201852317091835592374861144,266236010885685869904935495261864265,157899403462038839125137738939159318226008

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

%C 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).

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

%H Andrew Howroyd, <a href="/A052113/b052113.txt">Table of n, a(n) for n = 1..50</a>

%o (PARI)

%o 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}

%o 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]))}

%o a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^edges(p)); s/n!} \\ _Andrew Howroyd_, Sep 16 2018

%Y Cf. A004105, A047832.

%K nonn

%O 1,2

%A _Vladeta Jovovic_, Jan 21 2000

%E Terms a(14) and beyond from _Andrew Howroyd_, Sep 16 2018