The Number of Partitions of a Natural Number $n$ into Parts Each of which is not Less than $m$

We present recurrence formulas for the number of partitions of a natural number $n$ whose parts must be not less than $m$. A simple proof of Euler's formula for the number of partitions is given. We construct the triangle of partitions, put forward conjectures concerning the properties of the triangle, and propose an algorithm for calculating the partitions. An original graphical interpretation for the partition function is presented.