  A word $\sigma=\sigma_1...\sigma_n$ over the alphabet $[k]=\{1,2,...,k\}$ is
said to be {\em smooth} if there are no two adjacent letters with difference
greater than 1. A word $\sigma$ is said to be {\em smooth cyclic} if it is a
smooth word and in addition satisfies $|\sigma_n-\sigma_1|\le 1$. We find the
explicit generating functions for the number of smooth words and cyclic smooth
words in $[k]^n$, in terms of {\it Chebyshev polynomials of the second kind}.
Additionally, we find explicit formula for the numbers themselves, as
trigonometric sums. These lead to immediate asymptotic corollaries. We also
enumerate smooth necklaces, which are cyclic smooth words that are not
equivalent up to rotation.
