  Consider the multicolored urn model where, after every draw, balls of the
different colors are added to the urn in a proportion determined by a given
stochastic replacement matrix. We consider some special replacement matrices
which are not irreducible. For three- and four-color urns, we derive the
asymptotic behavior of linear combinations of the number of balls. In
particular, we show that certain linear combinations of the balls of different
colors have limiting distributions which are variance mixtures of normal
distributions. We also obtain almost sure limits in certain cases in contrast
to the corresponding irreducible cases, where only weak limits are known.
