$$U_{450}(x, y) = x + \frac{\sqrt{\frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}}}}{2} + \frac{1 - \sqrt{1 - 4 y}}{4 y}$$

$$T_{450}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}}}{n}&\text{if n>0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{2 k - n - 1}{n}} {\binom{- k - m + n - 1}{m - 1}}}{m} \end{cases} $$