login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003086 Number of self-complementary digraphs with n nodes.
(Formerly M3404)
9
1, 1, 4, 10, 136, 720, 44224, 703760, 179228736, 9168331776, 9383939974144, 1601371799340544, 6558936236286040064, 3837878966366932639744, 62879572771326489528942592, 128777257564337108286016980992 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, pp. 140, 243.
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
MATHEMATICA
Table[GraphPolynomial[n, x, Directed]/.x -> -1, {n, 1, 20}] (* Geoffrey Critzer, Oct 21 2012 *)
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_] := 4 Sum[Sum[GCD[v[[i]], v[[j]]], {j, 1, i - 1}], {i, 2, Length[v]}] + Sum[2 v[[i]] - 1, {i, 1, Length[v]}];
a[n_] := (s = 0; Do[s += permcount[2 p]*2^edges[p]*If[OddQ[n], n *4^Length[p], 1], {p, IntegerPartitions[n/2 // Floor]}]; s/n!);
Array[a, 16] (* Jean-François Alcover, Aug 26 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) = {4*sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, 2*v[i]-1)}
a(n) = {my(s=0); forpart(p=n\2, s+=permcount(2*Vec(p))*2^edges(p)*if(n%2, n*4^#p, 1)); s/n!} \\ Andrew Howroyd, Sep 16 2018
CROSSREFS
Sequence in context: A347818 A273517 A370687 * A102958 A321795 A220197
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Ronald C. Read and Vladeta Jovovic.
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 06:21 EDT 2024. Contains 370953 sequences. (Running on oeis4.)