So far you have shown only 10 terms of the sequence. How are we to know that the sequence doesn't go 1,0,0,1,0,0,0,0,1,0, 2, 2, 2, ... or 1,0,0,1,0,0,0,0,1,0, 1000000, 2000000, 3000000, ...?
In other words NO finite number of terms implies a specific rule. Unless there is more given in this problem, there is no way to know how it continues. Do have some reason to think there might be an exponential or similar rule? Of course, there exist a unique 9th degree polynomial equation that fits exactly those 10 points?