I think the sample locations would be (i + 1/2n, j + 1/2n), (i + 1/2n, j + 3/2n), ... ranging from i + 1/2n to i + (2n-1)/2n and j + 1/2n to j + (2n-1)/2n
I think the sample locations would be (i + 1/2n, j + 1/2n), (i + 1/2n, j + 3/2n), ... ranging from i + 1/2n to i + (2n-1)/2n and j + 1/2n to j + (2n-1)/2n