Generating function
$$U_{1029}(x, y) = \frac{\left(y + 1\right)^{3}}{1 - x}$$
Explicit formula
$$T_{1029}(n, m, k) = {\binom{3 k}{m}} {\binom{k + n - 1}{n}}$$
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
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