A005639 Number of self-converse oriented graphs with n nodes. (Formerly M1518)

1, 2, 5, 18, 102, 848, 12452, 265759, 10454008, 598047612, 63620448978, 9974635937844, 2905660724913768, 1268590412128132389, 1023130650177394611897, 1258149993547327488275562, 2834863110716120144290954314, 9900859865505110360978721901778

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.

Mathematica

permcount[v_] := Module[{m=1, s=0, k=0, t}, For[i=1, i <= Length[v], i++, t = v[[i]]; k = If[i>1 && t == v[[i-1]], k+1, 1]; m *= t*k; s += t]; s!/m];
edges[v_] := Sum[Sum[If[Mod[v[[i]] v[[j]], 2] == 0, GCD[v[[i]], v[[j]]], 0], {j, 1, i - 1}], {i, 2, Length[v]}] + Sum[If[Mod[v[[i]], 2] == 0, 2 Quotient[v[[i]] - 2, 4] + 1, 0], {i, 1, Length[v]}];
a[n_] := Module[{s = 0}, Do[s += permcount[p]*3^edges[p], {p, IntegerPartitions[n]}]; s/n!];
Array[a, 18] (* Jean-François Alcover, Aug 17 2019, after Andrew Howroyd *)

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: A322396 A007127 A279207 * A093730 A366449 A304918

Adjacent sequences: A005636 A005637 A005638 * A005640 A005641 A005642

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved