Let a_{n} be a sequence such that a_{1}=1 and a_{n+1}=\left\lfloor a_{n}+\sqrt{a_{n}}+\frac{1}{2}\right\rfloor, where \lfloor x\rfloor denotes the greatest integer less than or equal to x. What are the last four digits of a_{2012}?
Let a_{n} be a sequence such that a_{1}=1 and a_{n+1}=\left\lfloor a_{n}+\sqrt{a_{n}}+\frac{1}{2}\right\rfloor, where \lfloor x\rfloor denotes the greatest integer less than or equal to x. What are the last four digits of a_{2012}?