a(4) = 3 because there are 3 distinct 4 X 4 panmagic squares, not counting rotations, reflections, or row/column cyclings of others, with the additional property that each 2 X 2 square, including each "wrap around" 2 X 2 square such as the one consisting of a11, a12, a41, and a42, and the one consisting of a11, a14, a41, and a44, also sums to A006003(4) = 4(4^2+1)/2 = 34:
1 8 10 15 1 8 11 14 1 8 13 12
12 13 3 6 12 13 2 7 14 11 2 7
7 2 16 9 6 3 16 9 4 5 16 9
14 11 5 4 15 10 5 4 15 10 3 6
The following panmagic square does not count because it can be formed from the third panmagic square given above by moving the first column on the left of it to the right of it and then reflecting it in the yaxis:
1 12 13 8
14 7 2 11
4 9 16 5
15 6 3 10
