I am a high school student who is interested in mathematics, and I'm stuck on a problem while doing a small investigation (too small to be called "research").
Problem: what is the sum of all elements of $n \times n$ matrix $M^m$, where $M_{ij} = \begin{cases} 0, & j > i + 1 \\ 1, & j \le i + 1 \end{cases} ?$
Although answers in terms of $m, n$ are better, other forms would help.
Thanks in advance!