Find a formula for nth term of {an}, if the first 10 terms ...?

There is no single correct answer. Notice the 1, then 2 0's, 1, 4 0's, 1, what next? 6 0's or 8 0's? Either is possible. Or you could have a 1 at position 1, 1 at position 4, 1 at position 9, and so a 1 at any position that's a perfect square with 0's everywhere else. This would not be the same as either of the 1st 2 patterns.