We present neutrino mass matrix textures in a minimal framework of the type-I seesaw mechanism, where two right-handed Majorana neutrinos are introduced in order to reproduce experimental results of neutrino oscillations. The textures can lead to experimentally favored leptonic mixing angles described by tri-bimaximal mixing with one additional rotation. We present minimal and next to minimal textures for the normal mass hierarchy case in the context of the texture zero. A minimal texture in the inverted hierarchy case is also constructed, which does not have any vanishing entries in a Dirac neutrino mass matrix. We also discuss some cases in which the model parameters in the textures are supposed to be a neutrino mass ratio and/or the Cabibbo angle. Predicted regions of mixing angles, a leptonic CP-violation parameter, and an effective mass for the neutrinoless double beta decay are presented in all textures.
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