>>291
a[n]=a[n+1]-a[n+2]+n
　　 =(a[n+2]-a[n+3]+n+1)-a[n+2]+n
　　 =-a[n+3]+2n+1
　　 =-(a[n+4]-a[n+5]+n+3)+2n+1
　　 =a[n+5]-a[n+4]+n-2
　　 =a[n+6]-6

∴a[n+6]-a[n]=6

上で導いた　a[n]+a[n+3]=2n+1より
a[n+1]+a[n+4]=2n+3,
a[n+2]+a[n+5]=2n+5　　3式の両辺を加えると

　 a[n]+a[n+1]+a[n+2]+a[n+3]+a[n+4]　+a[n+5] =6n+9
a[n+6]　+a[n+7] +a[n+8]　+a[n+9] +a[n+10]+a[n+11]=6n+45
a[n+12]+a[n+13]+a[n+14]+a[n+15]+a[n+16]+a[n+17]=6n+81
…
a[n+55]+a[n+56]+a[n+57]+a[n+58]+a[n+59]+a[n+60]=6n+339

上式の右辺にn=1を代入して加えると、
15+51+87+123+159+195+231+267+303+339=1770

∴Σ[k=1,60](a[k])=1770