1 research outputs found
Counting Colorful Necklaces and Bracelets in Three Colors
A necklace or bracelet is \textit{colorful} if no pair of adjacent beads are
the same color. In addition, two necklaces are \textit{equivalent} if one
results from the other by permuting its colors, and two bracelets are
\textit{equivalent} if one results from the other by either permuting its
colors or reversing the order of the beads; a bracelet is thus a necklace that
can be turned over. This note counts the number of non-equivalent
colorful necklaces and the number of colorful bracelets formed with
-beads in at most three colors. Expressions obtained for simplify
expressions given by OEIS sequence A114438, while the expressions given for
appear to be new and are not included in OEIS.Comment: 19 pages, 2 figure