本帖最后由 tommywong 于 2014-1-28 21:50 编辑
大突破!无单位根公式:
$\displaystyle\sum_{k=0}^n C_{a+dk}^m=\sum_{r=0}^{d-1} (C_{m+1+n+[\frac{a}{d}]-r}^{m+1}-C_{m+[\frac{a}{d}]-r}^{m+1})\sum_{k=0}^{m+1} (-1)^k C_{m+1}^k C_{m+(a-m)remd+dr-dk}^m$
$\displaystyle\sum_{k=0}^2 C_{3+7k}^3=\sum_{r=0}^6 C_{6-r}^4 \sum_{k=0}^4 (-1)^k C_4^k C_{3+7r-7k}^3=C_6^4+(C_{10}^3-4C_3^3)C_5^4+(C_{17}^3-4C_{10}^3+6C_3^3)C_4^4=15+(116)5+206=801$ |