MathNet 2017-part-04 — 176 problems (EN–VI) Question 106

Let $\lfloor x\rfloor$ denote the greatest integer less than or equal to $x$. If $a_{n}\lfloor a_{n}\rfloor=49^{n}+2 n+1$, find the value of $2 S+1$, where $S=\left\lfloor\sum_{n=1}^{2017} \frac{a_{n}}{2}\right\rfloor$.