Generating function
$$U_{928}(x, y) = \sqrt{x^{2} + 4 x y + 2 x + 4 y + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{928}(n, m, k) = \operatorname{Tsqrt}{\left(m,k \right)} {\binom{k - m}{n}}$$
1 | 2 | -2 | 4 | -10 | 28 | -84 |
1 | 0 | 2 | -8 | 30 | -112 | 420 |
0 | 0 | -2 | 12 | -60 | 280 | -1260 |
0 | 0 | 2 | -16 | 100 | -560 | 2940 |
0 | 0 | -2 | 20 | -150 | 980 | -5880 |
0 | 0 | 2 | -24 | 210 | -1568 | 10584 |
0 | 0 | -2 | 28 | -280 | 2352 | -17640 |
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