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%I #16 Aug 15 2019 21:34:31
%S 1,1,0,6,48,1020,32232,2097144,268369920,68719472640,35184338533920,
%T 36028797018963936,73786976226114539520,302231454903657293676480,
%U 2475880078570197599844819072,40564819207303340847860140736640,1329227995784915854457062986570792960
%N Number of simple graphs with n vertices and distinct rotations.
%C 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. These are different from aperiodic graphs and acyclic graphs but are similar to aperiodic sequences (A000740) and aperiodic arrays (A323867).
%H Andrew Howroyd, <a href="/A324461/b324461.txt">Table of n, a(n) for n = 0..50</a>
%H Gus Wiseman, <a href="/A324461/a324461.png">The a(4) = 48 graphs with distinct rotations</a>.
%F a(n > 0) = A306715(n) * n.
%F a(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
%t rotgra[g_,m_]:=Sort[Sort/@(g/.k_Integer:>If[k==m,1,k+1])];
%t Table[Length[Select[Subsets[Subsets[Range[n],{2}]],UnsameQ@@Table[Nest[rotgra[#,n]&,#,j],{j,n}]&]],{n,0,5}]
%o (PARI) a(n)={if(n==0, 1, sumdiv(n, d, moebius(d)*2^(n*(n/d-1)/2 + n*(d\2)/d)))} \\ _Andrew Howroyd_, Aug 15 2019
%Y Cf. A000088, A000740, A003436, A006125, A027375, A192314, A192332, A306669, A306715, A323860, A323864, A323867, A324462 (covering case), A324463, A324464.
%K nonn
%O 0,4
%A _Gus Wiseman_, Feb 28 2019
%E Terms a(7) and beyond from _Andrew Howroyd_, Aug 15 2019
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