Generating function
$$U_{1020}(x, y) = \frac{\left(x + 1\right)^{3}}{1 - y}$$
Explicit formula
$$T_{1020}(n, m, k) = {\binom{3 k}{n}} {\binom{k + m - 1}{m}}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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