The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A324462 Number of simple graphs covering n vertices with distinct rotations. 7
 1, 0, 0, 3, 28, 765, 26958, 1887277, 252458904, 66376420155, 34508978662350, 35645504882731557, 73356937843604425644, 301275024444053951967585, 2471655539736990372520379226, 40527712706903544100966076156895, 1328579255614092949957261201822704816 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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. It is covering if there are no isolated vertices. These are different from aperiodic graphs and acyclic graphs but are similar to aperiodic sequences (A000740) and aperiodic arrays (A323867). LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 Gus Wiseman, The a(4) = 28 graph covers with distinct rotations. FORMULA a(n) = Sum{d|n} mu(n/d) * Sum_{k=0..d} (-1)^(d-k)*binomial(d,k)*2^( k*(k-1)*n/(2*d) + k*(floor(n/(2*d))) ) for n > 0. - Andrew Howroyd, Aug 19 2019 MATHEMATICA rotgra[g_, m_]:=Sort[Sort/@(g/.k_Integer:>If[k==m, 1, k+1])]; Table[Length[Select[Subsets[Subsets[Range[n], {2}]], And[Union@@#==Range[n], UnsameQ@@Table[Nest[rotgra[#, n]&, #, j], {j, n}]]&]], {n, 0, 5}] PROG (PARI) a(n)={if(n<1, n==0, sumdiv(n, d, moebius(n/d)*sum(k=0, d, (-1)^(d-k)*binomial(d, k)*2^(k*(k-1)*n/(2*d) + k*(n/d\2)))))} \\ Andrew Howroyd, Aug 19 2019 CROSSREFS Cf. A000088, A000740, A002494, A006125, A006129, A027375, A192332, A323863, A323864, A323867, A323869, A324461 (non-covering case), A324463, A324464. Sequence in context: A110259 A276745 A015474 * A053601 A328791 A140990 Adjacent sequences:  A324459 A324460 A324461 * A324463 A324464 A324465 KEYWORD nonn AUTHOR Gus Wiseman, Feb 28 2019 EXTENSIONS Terms a(7) and beyond from Andrew Howroyd, Aug 19 2019 STATUS approved

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

Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)