KMO 1997 Problem 2

For positive integer $n,$ let $a_n=\sum_{k=0}^{[\frac{n}{2}]}\binom{n-2}{k}(-\frac{1}{4})^k.$ Find $a_{1997}.$ (For real $x,$ $[x]$ is defined as largest integer that does not exceeds $x.$ )