How this calculation works
Count cyclic bead colorings with rotations identified.
THE FORMULA
Average colors^gcd(n,k) over all n rotationsA worked example
Four beads and two colors give (16+2+4+2)/4 = 6.
Good to know
Mirror reflections are treated as distinct unless rotation identifies them.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count cyclic bead colorings with rotations identified.
The primary result is labeled “Colorings”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Mirror reflections are treated as distinct unless rotation identifies them.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Four beads and two colors give (16+2+4+2)/4 = 6.
Which rule does this calculator apply?
Average colors^gcd(n,k) over all n rotations