Non-Abelian quantized Hall states of electrons at filling factors 12/5   and 13/5 in the first excited Landau level
  We present results of extensive numerical calculations on the ground state of electrons in the first excited (n=1) Landau level with Coulomb interactions, and including non-zero thickness effects, for filling factors 12/5 and 13/5 in the torus geometry. In a region that includes these experimentally-relevant values, we find that the energy spectrum and the overlaps with the trial states support the previous hypothesis that the system is in the non-Abelian k = 3 liquid phase we introduced in a previous paper. 
E.H. Rezayi and N. Read