Generating function
$$U_{103}(x, y) = \frac{2 y + \sqrt{x^{2} - 2 x + 4 y^{2} + 1}}{x^{2} - 2 x + 1}$$
Explicit formula
$$T_{103}(n, m, k) = \frac{4^{m} k {\binom{\frac{k}{2} + \frac{m}{2}}{\frac{k}{2} - \frac{m}{2}}} {\binom{k + m + n - 1}{n}}}{k + m}$$
1 | 2 | 16/3 | 0 | 0 | 0 | 0 |
1 | 4 | 16 | 0 | 0 | 0 | 0 |
1 | 6 | 32 | 0 | 0 | 0 | 0 |
1 | 8 | 160/3 | 0 | 0 | 0 | 0 |
1 | 1 | 8 | 0 | 0 | 0 | 0 |
1 | 12 | 112 | 0 | 0 | 0 | 0 |
1 | 14 | 448/3 | 0 | 0 | 0 | 0 |
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