From the meaning of the question, we know that a 1= 1, a2=6, a3= 15, a4=28, a5=45, a6=66, …;

∴a2-a 1=5,a3-a2=9,a4-a3= 13,a5-a4= 17,a6-a5=2 1,…,an-an- 1=4n-3；

∴(a2-a 1)+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)+…+(an-an- 1)

= an-a 1 = 5+9+ 13+ 17+2 1+…+(4n-3)=(n？ 1)(5+4n？ 3)2 = 2 N2-n- 1；

∴an=2n2-n，

So the answer is: 2n2-n.