$$U_{648}(x, y) = \frac{\left(\sqrt{4 x + 1} + 1\right) \left(\sqrt{4 y + 1} + 1\right)}{4}$$

$$T_{648}(n, m, k) = \begin{cases}1&\text{if n==0, m==0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 2 m - 1}{m - 1}}}{m}&\text{if n==0, m>0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if m==0, n>0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(-1\right)^{n - 1} k^{2} {\binom{- k + 2 m - 1}{m - 1}} {\binom{- k + 2 n - 1}{n - 1}}}{m n}&\text{if n>0, m>0} \end{cases} $$