  Using a variational method we study a sequence of the one-electron atomic and
molecular-type systems H, H_2^+, H_3^(2+) and H_4^(3+) in the presence of a
homogeneous magnetic field ranging B = 0 - 4.414x10^{13} G. These systems are
taken as a linear configuration aligned with the magnetic lines. For H_3^(2+)
the potential energy surface has a minimum for B\sim 10^{11} G which deepens
with growth of the magnetic field strength (JETP Lett. 69, 844 (1999)); for B
\gtrsim 10^{12} G the minimum of the potential energy surface becomes
sufficiently deep to have longitudinal vibrational state. We demonstrate that
for the (ppppe) system the potential energy surface at B \gtrsim 4.414x10^{13}
G develops a minimum, indicating the possible existence of exotic molecular ion
H_4^(3+). We find that for almost all accessible magnetic fields H_2^+ is the
most bound one-electron linear system while for magnetic fields B \gtrsim
10^{13} G the molecular ion H_3^(2+) becomes the most bound.
