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 A203398 T(n,k), a triangular array read by rows, is the number of classes of equivalent 2-color n-bead necklaces (turning over is not allowed) that have k necklaces. 1
 2, 2, 1, 2, 0, 2, 2, 1, 0, 3, 2, 0, 0, 0, 6, 2, 1, 2, 0, 0, 9, 2, 0, 0, 0, 0, 0, 18, 2, 1, 0, 3, 0, 0, 0, 30, 2, 0, 2, 0, 0, 0, 0, 0, 56, 2, 1, 0, 0, 6, 0, 0, 0, 0, 99, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 186, 2, 1, 2, 3, 0, 9, 0, 0, 0, 0, 0, 335 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, the cyclic group of order n acts on the set of length n binary sequences.  T(n,k) is the number of orbits that have k elements. LINKS Frank Ruskey, Combinatorial Generation Algorithm Algorithm 4.24, p. 95. EXAMPLE 2   2  1   2  0  2   2  1  0  3   2  0  0  0  6   2  1  2  0  0  9   2  0  0  0  0  0  18   2  1  0  3  0  0  0  30   2  0  2  0  0  0  0  0  56   2  1  0  0  6  0  0  0  0  99   2  0  0  0  0  0  0  0  0  0  186   2  1  2  3  0  9  0  0  0  0  0   335 MATHEMATICA Needs["Combinatorica`"]; f[list_] := Sort[NestList[RotateLeft, list, Length[list]-1]]; Flatten[Table[Distribution[Map[Length, Map[Union, Union[Map[f, Strings[{0, 1}, n]]]]], Range[n]], {n, 1, 12}]] CROSSREFS A000031 (row sums), T(n,n) = A001037, T(n,n) = A064535 when n is prime, T(n,k) = A001037(k) when k divides n. Cf. A203399. Sequence in context: A104405 A156381 A089077 * A225064 A130071 A321373 Adjacent sequences:  A203395 A203396 A203397 * A203399 A203400 A203401 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Jan 01 2012 STATUS approved

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)