$$U_{437}(x, y) = x + \frac{\sqrt{4 y + 1}}{4} + \frac{\sqrt{2 x \left(\sqrt{4 y + 1} + 1\right) + \frac{\left(\sqrt{4 y + 1} + 1\right)^{2}}{4}}}{2} + \frac{1}{4}$$

$$T_{437}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}}}{n}&\text{if n>0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{2 k - n - 1}{n}} {\binom{- k + 2 m + n - 1}{m - 1}}}{m} \end{cases} $$