NumberOfNecklaces[n, nc, Cyclic] returns the number of distinct ways in which an -bead necklace can be colored with nc colors, assuming that two colorings are equivalent if one can be obtained from the other by a rotation.
NumberOfNecklaces[n, nc, Dihedral] returns the number of distinct ways in which an -bead necklace can be colored with nc colors, assuming that two colorings are equivalent if one can be obtained from the other by a rotation or a flip.