$$U_{603}(x, y) = \frac{4 x + \frac{\left(\sqrt{4 y + 1} + 1\right)^{3}}{2}}{\left(\sqrt{4 y + 1} + 1\right)^{2}}$$

$$T_{603}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m==0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - 3 n\right) {\binom{k}{n}} {\binom{- k + 2 m + 3 n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$