login
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
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.
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 * A339275 A225064 A361967
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jan 01 2012
STATUS
approved