NumberOfNecklaces

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.