  The equivalence is established between the one-dimensional (1D) Bose-system
with a finite number of particles and the system obeying the fractional
(intermediate) Gentile statistics, in which the maximum occupation of
single-particle energy levels is limited. The system of 1D harmonic oscillators
is considered providing the model of harmonically trapped Bose-gas. The results
are generalized for the system with power energy spectrum.
