Generating function
$$U_{1002}(x, y) = \left(x + 1\right) \left(y + 1\right)^{3}$$
Explicit formula
$$T_{1002}(n, m, k) = {\binom{k}{n}} {\binom{3 k}{m}}$$
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 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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