TITLE: Minimal words of length n
QUESTION [7 upvotes]: Let W be a finite word on a two symbol alphabet {0,1}; let us say that W is maximal if it is the last item in the list of all its cyclic permutation (ordered lexicographically).
So, for instance:
{0,1}         are the maximal words of length 1;
{00, 10, 11}  are the maximal words of length 2;
{000, 100, 110, 111}    are the maximal words of length 3;
{0000, 1000, 1010, 1100, 1110, 1111} are the maximal words of length 4;
{00000, 10000, 10100, 11000, 11010, 11100, 11110, 11111} are the maximal words of length 5; ...
und so weiter.
Let 
k(n):= number of maximal words of length n
Is there some formula for k(n)?

REPLY [6 votes]: please see wikipedia :  http://en.wikipedia.org/wiki/Necklace_(combinatorics)
It represents a structure with n circularly connected beads of up to k different colors or numbers.