  We study the nature of one-electron eigen-states in a one-dimensional diluted
Anderson model where every Anderson impurity is diluted by a periodic function
$f(l)$ . Using renormalization group and transfer matrix techniques, we provide
accurate estimates of the extended states which appear in this model, whose
number depends on the symmetry of the diluting function $f(l)$. The density of
states (DOS) for this model is also numerically obtained and its main features
are related to the symmetries of the diluting function $f(l)$. Further, we show
that the emergence of extended states promotes a sub-diffusive spread of an
initially localized wave-packet.
