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