Yet another counting problem

This seems to fall for computation, I am looking at a possible elegant solution.

Problem:Let us have a n*n square.Two squares(both of dimension less than n*n)form an unordered pair if

(i) They have atleast one 1*1 square common.

(ii)One is not contained in the other.

Compute the number of unordered pairs.

(nothing sacred about squares, rectangles must make the problem tougher)