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A052112 Number of self-complementary directed 2-multigraphs on n nodes. 3
1, 2, 14, 159, 7629, 599456, 226066304, 139178815861, 410179495378288, 2055126126323159298, 48234291396964332998082, 2016523952125103590736221923, 382812826011951187177138562992638, 135681830960694827549160289095792266106 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

LINKS

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

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) = {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]-1))}

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

CROSSREFS

Cf. A053467, A003086, A053588.

Sequence in context: A196791 A218295 A268011 * A074635 A201465 A245894

Adjacent sequences:  A052109 A052110 A052111 * A052113 A052114 A052115

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jan 21 2000

EXTENSIONS

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

STATUS

approved

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Last modified October 19 14:21 EDT 2018. Contains 316362 sequences. (Running on oeis4.)