Am gasit ceea ce ai gresit si am rescris putin codul tau. Am mai adaugat un vector si am inlocuit aux cu c. Succes!
#include <bits/stdc++.h>
using namespace std;
ifstream fin("sirul.in");
ofstream fout("sirul.out");
char a[10005] = "a", b[10005] = "b", c[10005];
int n, k;
int main()
{
fin>>n;
strcpy(c, b);
strcat(b, a);
k=2;
while(k!=n)
{
strcpy(a, c);
strcpy(c, b);
strcat(b, a);
k++;
}
fout<<c;
}