OFFSET
1,3
COMMENTS
A simple graph with n vertices has distinct rotations if all n rotations of its vertex set act on the edge set to give distinct graphs. A graphical necklace is a simple graph that is minimal among all n rotations of the vertices.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..50
FORMULA
a(n > 0) = A324461(n)/n.
a(n) = (1/n)*Sum_{d|n} mu(d)*2^(n*(n/d-1)/2 + n*floor(d/2)/d) for n > 0. - Andrew Howroyd, Aug 15 2019
MATHEMATICA
rotgra[g_, m_]:=Sort[Sort/@(g/.k_Integer:>If[k==m, 1, k+1])];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], With[{rots=Table[Nest[rotgra[#, n]&, #, j], {j, n}]}, UnsameQ@@rots&&#==First[Sort[rots]]]&]], {n, 5}]
PROG
(PARI) a(n)={if(n==0, 1, sumdiv(n, d, moebius(d)*2^(n*(n/d-1)/2 + n*(d\2)/d))/n)} \\ Andrew Howroyd, Aug 15 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 05 2019
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Aug 15 2019
STATUS
approved