Some solutions for n=4
..x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1
..1..x..2..x....1..x..2..x....1..x..2..x....1..x..2..x....1..x..2..x
..x..0..x..1....x..0..x..3....x..0..x..3....x..0..x..3....x..0..x..3
..1..x..3..x....2..x..4..x....3..x..4..x....3..x..2..x....4..x..1..x
..x..4..x..5....x..0..x..5....x..5..x..1....x..4..x..5....x..5..x..2
..0..x..3..x....5..x..6..x....1..x..6..x....3..x..6..x....0..x..4..x
..x..4..x..6....x..7..x..5....x..0..x..4....x..2..x..0....x..1..x..3
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