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.
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.
Details and Options
- To use NumberOfNecklaces, you first need to load the Combinatorica Package using Needs["Combinatorica`"].
Text
Wolfram Research (2012), NumberOfNecklaces, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/NumberOfNecklaces.html.
CMS
Wolfram Language. 2012. "NumberOfNecklaces." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/NumberOfNecklaces.html.
APA
Wolfram Language. (2012). NumberOfNecklaces. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/NumberOfNecklaces.html