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A005639 Number of self-converse oriented graphs with n nodes.
(Formerly M1518)
3
1, 2, 5, 18, 102, 848, 12452, 265759, 10454008, 598047612, 63620448978, 9974635937844, 2905660724913768, 1268590412128132389, 1023130650177394611897, 1258149993547327488275562, 2834863110716120144290954314, 9900859865505110360978721901778 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

R. W. Robinson, Asymptotic number of self-converse oriented graphs, pp. 255-266 of Combinatorial Mathematics (Canberra, 1977), Lect. Notes Math. 686, 1978.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..50 (terms 1..27 from R. W. Robinson)

R. W. Robinson, Asymptotic number of self-converse oriented graphs, pp. 255-266 of Combinatorial Mathematics (Canberra, 1977), Lect. Notes Math. 686, 1978. (Annotated scanned copy)

Sridharan, M. R., Self-complementary and self-converse oriented graphs , Nederl. Akad. Wetensch. Proc. Ser. A 73=Indag. Math. 32 1970 441-447. [Annotated scanned copy] See page 446.

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) = {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]-2)\4*2+1))}

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

CROSSREFS

Cf. A002785.

Sequence in context: A075634 A007127 A279207 * A093730 A304918 A007769

Adjacent sequences:  A005636 A005637 A005638 * A005640 A005641 A005642

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 18 16:23 EST 2018. Contains 317323 sequences. (Running on oeis4.)