Matrix & Partition & Natural Number & Pattern

I would like to know if someone know, how is called a matrix M*N, where m represents the row index in the matrix and the sum of the N columns at this row. Meaning that each row represents a possible partition of m into N parts. Finally the sum of the matrix is always a triangular number.

e.g.
0 0 1
0 1 1
1 1 1
2 1 1

As well, if you have informations about evaluation of those type of Matrix, that would be great, e.g. discrepancy, distribution, pattern... whatever

Thanks a lot

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If I understand your description of the matrix correctly, then $M$ is the row index and $N$ is the total number of columns. That seems like a rather unusual and confusing choice of variables, especially in connection with calling this sort of thing "a rectangular matrix M*N", which sounds a lot like you mean an $M\times N$ matrix. I would suggest to use uppercase letters $M$ and $N$ to denote the total numbers of rows and columns, respectively, and lowercase letters, e.g. $i$ and $j$, or, if you prefer, $m$ and $n$, to denote the indices. – joriki Jun 5 '12 at 11:49
Thanks for the precision joriki! – Triton Jun 5 '12 at 12:06