Generating function
$$U_{900}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2 \operatorname{abs}{\left(y - 1 \right)}} \right)}}{3} \right)}}{3 x \left(1 - y\right)}$$
Explicit formula
$$T_{900}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{3 k + m + 2 n - 1}{m}}}{k + n}$$
1 | 3 | 6 | 1 | 15 | 21 | 28 |
2 | 1 | 3 | 7 | 14 | 252 | 42 |
7 | 49 | 196 | 588 | 147 | 3234 | 6468 |
3 | 27 | 135 | 495 | 1485 | 3861 | 9009 |
143 | 1573 | 9438 | 40898 | 143143 | 429429 | 1145144 |
728 | 9464 | 66248 | 33124 | 132496 | 4504864 | 13514592 |
3876 | 5814 | 46512 | 263568 | 1186056 | 45070128 | 15023376 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #900?