$$U_{649}(x, y) = \frac{x \left(\sqrt{4 y + 1} + 1\right)^{2}}{4} + \frac{\sqrt{4 y + 1}}{2} + \frac{1}{2}$$

$$T_{649}(n, m, k) = \begin{cases}1&\text{if n==0, m==0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 2 m - n - 1}{m - 1}}}{m}&\text{if n==0, m>0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + n - 1}{n - 1}}}{n}&\text{if m==0, n>0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(-1\right)^{n - 1} k \left(k + n\right) {\binom{- k + n - 1}{n - 1}} {\binom{- k + 2 m - n - 1}{m - 1}}}{m n}&\text{if n>0, m>0} \end{cases} $$