2 : {1, 2, 3, 4}
3 : {1,2,3,4,4,3,2,1}
4 : {1,2,3,4,5,6,7,8,8,7,6,5,4,3,2,1}
5 : {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1}
6 : {1,14,10,2,16,7,11,13,8,6,12,12,6,10,5,8,3,7,15,4,15,2,3,5,13,9,11,16,4,9,14,1,5,11,9,1,14,13,9,4,4,15,7,3,16,3,2,15,10,8,6,16,12,12,8,6,2,5,13,14,1,11,7,10}
7 : {6,13,16,4,7,9,4,12,15,3,10,7,14,5,17,4,1,2,16,15,12,17,13,3,17,11,5,6,7,10,13,14,3,16,8,8,2,10,9,2,17,5,12,11,5,14,15,11,6,10,8,7,16,15,2,17,9,8,4,1,13,1,14,3,17,17,5,14,11,15,12,1,10,16,2,10,8,16,1,17,5,14,15,7,6,8,11,17,4,12,9,9,13,2,3,8,3,3,11,13,9,17,1,6,4,1,17,13,7,6,6,15,14,12,14,7,11,4,10,5,15,2,17,9,13,12,16,16}

The integers below indicate the dominating sets via inverse inverses. E.g, in the case of n = 4, the inverse images are in positions as follows

{1, 8}, {2, 7}, {3, 6}, {4, 5}

Subtracting 1 because we wish the vertices to be from 0 to 7 gives

{0, 7}, {1, 6}, {2, 5}, {3, 4}

and writing these in binary gives the four dominating sets in terms of bit-strings

{000, 111}    {001, 101}     {010, 101}     {011, 100}

These have length 3 because the halved cube graph for n = 4 is isomorphic to the Hamming radius-2 graphs for n = 3.

3 : {1, 2, 3, 4}
4 : {1,2,3,4,4,3,2,1}
5 : {1,2,3,4,5,6,7,8,8,7,6,5,4,3,2,1}
6 : {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1}
7 : {1,14,10,2,16,7,11,13,8,6,12,12,6,10,5,8,3,7,15,4,15,2,3,5,13,9,11,16,4,9,14,1,5,11,
         9,1,14,13,9,4,4,15,7,3,16,3,2,15,10,8,6,16,12,12,8,6,2,5,13,14,1,11,7,10}
8 : {6,13,16,4,7,9,4,12,15,3,10,7,14,5,17,4,1,2,16,15,12,17,13,3,17,11,5,6,7,10,13,14,3,
        16,8,8,2,10,9,2,17, 5,12,11,5,14,15,11,6,10,8,7,16,15,2,17,9,8,4,1,13,1,14,3,17,17,
        5,14,11,15, 12,1,10,16,2,10,8,16,1,17,5,14,15,7,6,8,11,17,4,12,9,9,13,2,3,8,3,3,11,13,9,17,
        1,6,4,1,17,13,7,6,6,15,14,12,14,7,11,4,10,5,15,2,17,9,13,12,16,16}