Generating function
$$U_{524}(x, y) = x + y^{3} + 3 y^{2} + y \left(x + 3\right) + 1$$
Explicit formula
$$T_{524}(n, m, k) = {\binom{k}{n}} {\binom{3 k - 2 n}{m}}$$
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 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 | 0 | 0 |
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