(n-1)²+n²+(n+1)²=3n²+2*1²
(n-2)²+(n-1)²+n²+(n+1)²+(n+2)²=5n²+2*2²+2*1²=5n²+2*(2²+1²)
51*51+52*52+53*53+.+99*99
=(75-24)²+(75-23)²+..+75²+..+(75+23)²+(75+24)²
=49*75²+2*(24²+23²+.+2²+1²)
=49*75²+2*(24²+23²+.+2²)+2
=49*75²+2*[23*13²+2*(11²+10²+1²)]+2
=49*75²+2*23*13²+4*[11*6²+2*(5²+4²+3²+2²+1²)]+2
=49*75²+2*23*13²+4*11*6²+8*[5*3²+2*(2²+1²)]+2
=49*75²+2*23*13²+4*11*6²+8*5*3²+16*5+2
然后就先算乘法再算加法!
暂时没有找到其他规律!