An accurate study of the lowest 1σ_g and the low-lying excited 1σ_u, 1π_u,g, 1δ_g,u electronic states of the exotic molecular ion H_3^2+ in linear configuration parallel to a magnetic field is carried out. The magnetic field ranges from 10^10 G up to 4.414 × 10^13 G where non-relativistic considerations are justified. The variational method is exploited and the same trial function is used for different magnetic fields. It is shown that the states of positive z-parity 1σ_g, 1π_u, 1δ_g are bound

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... tates of the H_3^2+ exotic ion for all magnetic fields studied. We also demonstrate that for magnetic fields B≳ 2.35× 10^12 G the potential energy surface well corresponding to the 1σ_g state contains at least one longitudinal vibrational state. It is also shown that the negative z-parity states 1σ_u, 1π_g, 1δ_u, are purely repulsive in the whole range of magnetic fields studied, B=10^10- 4.414 × 10^13 G.