Squaring numbers made up of 1s

1. Choose a a number made up of ones (up to nine digits).
2. The answer will be a series of consecutive digits beginning with 1, up to the number of ones in the given number, and back to 1.

Example:

1. If the number is 11111, (5 digits) -
2. The square of the number is 123454321.
   (Begin with 1, up to 5, then back to 1.)