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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.

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