$$U_{444}(x, y) = x + \frac{\left(y + 1\right)^{2}}{2} - \frac{\sqrt{4 x \left(y + 1\right)^{2} + \left(y + 1\right)^{4}}}{2}$$

$$T_{444}(n, m, k) = \begin{cases}1&\text{if n<2*k} ,\ \\- \frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\- \frac{2 k {\binom{2 k - 2 n - 1}{m - 1}} {\binom{2 k - n - 1}{n}}}{m}&\text{if m>0} \end{cases} $$