2^(n+1)-2

One fact is the symmetry. So assume the upper left corner of the n*n board is white. Then recursive formula can be found by considering the 3 cases. 1.no black 1*2 block but has black 2*1 blocks. 2. no black 2*1 blocks but has black 1*2 blocks. 3. neither black 1*2 nor 2*1 blocks exist.