  Quantum walks behave differently from what we expect and their probability
distributions have unique structures. They have localization, singularities, a
gap, and so on. Those features have been discovered from the view point of
mathematics and reported as limit theorems. In this paper we focus on a
time-dependent three-state quantum walk on the line and demonstrate a limit
distribution. Three coin states at each position are iteratively updated by a
coin-flip operator and a position-shift operator. As the result of the
evolution, we end up to observe both localization and a gap in the limit
distribution.
