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 A086675 Number of n X n (0,1)-matrices modulo cyclic permutations of the rows. 8
 1, 2, 10, 176, 16456, 6710912, 11453291200, 80421421917440, 2305843009750581376, 268650182136584290872320, 126765060022823052739661424640, 241677817415439249618874010960064512, 1858395433210885261795036719974526548094976 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also the number of digraphical necklaces with n vertices. A digraphical necklace is defined to be a directed graph that is minimal among all n rotations of the vertices. Alternatively, it is an equivalence class of directed graphs under rotation of the vertices. These are a kind of partially labeled digraphs. - Gus Wiseman, Mar 04 2019 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..57 FORMULA a(n) = (1/n)*Sum_{ d divides n } phi(d)*2^(n^2/d) for n > 0, a(0) = 1. EXAMPLE From Gus Wiseman, Mar 04 2019: (Start) Inequivalent representatives of the a(2) = 10 digraphical necklace edge-sets:   {}   {(1,1)}   {(1,2)}   {(1,1),(1,2)}   {(1,1),(2,1)}   {(1,1),(2,2)}   {(1,2),(2,1)}   {(1,1),(1,2),(2,1)}   {(1,1),(1,2),(2,2)}   {(1,1),(1,2),(2,1),(2,2)} (End) MATHEMATICA Table[Fold[ #1+EulerPhi[ #2] 2^(n^2 /#2)&, 0, Divisors[n]]/n, {n, 16}] (* second program *) rotdigra[g_, m_]:=Sort[g/.k_Integer:>If[k==m, 1, k+1]]; Table[Length[Select[Subsets[Tuples[Range[n], 2]], #=={}||#==First[Sort[Table[Nest[rotdigra[#, n]&, #, j], {j, n}]]]&]], {n, 0, 4}] (* Gus Wiseman, Mar 04 2019 *) CROSSREFS Cf. A000031 (binary necklaces), A000939 (cycle necklaces), A008965, A060690, A061417 (permutation necklaces), A184271, A192332 (graphical necklaces), A275527 (path necklaces), A323858 (toroidal necklaces), A323870. Cf. A324463, A324464, A324513, A324514. Sequence in context: A132341 A069994 A063573 * A319607 A057119 A226563 Adjacent sequences:  A086672 A086673 A086674 * A086676 A086677 A086678 KEYWORD nonn,easy AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 27 2003 EXTENSIONS More terms from Wouter Meeussen, Jul 29 2003 a(0)=1 prepended by Gus Wiseman, Mar 04 2019 STATUS approved

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Last modified August 10 06:08 EDT 2022. Contains 356029 sequences. (Running on oeis4.)