  In the paper, the quantum-statistical approach is used to estimate the number
of restricted plane partitions of an integer $n$ with the number of parts not
exceeding some finite $N$. The analogy between this number-theoretical problem
and the enumeration of microstates of the ideal two-dimensional Bose-gas is
used. The conjectured expression for the number of restricted plane partitions
shows a good agreement between calculated and exact values for $n=10\div20$.
