  In this paper, the statistical-mechanical entropies of 5D Ricci-flat black
string is calculated through the wave modes of the quantum field with improved
thin-layer brick-wall method. The modes along the fifth dimension are
semi-classically quantized by Randall-Sundrum mass relationship. We use the
two-dimensional area to describe this black string's entropy which, in the
small-mass approximation, is a linear sum of the area of the black hole horizon
and the cosmological horizon. The proportionality coefficients of entropy are
discretized with quantized extra dimensional modes. It should be noted that the
small-mass approximation used in our calculation is naturally justified by the
assumption that the two branes are located far apart.
