A215293
Number of permutations of 0..floor((n*n-2)/2) on odd squares of an n X n array such that each row and column of odd squares is increasing.
Original entry on oeis.org
1, 2, 6, 280, 23100, 85765680, 577185873264, 346915095471584640, 381134230556959188429120, 62144711688730139887005809020800, 18592619468814454675301397184588597886400, 1236552808693429892089668394551052130596983991526400, 151213938214745201135492692441902799026853717717324113365952000
Offset: 1
Some solutions for n=5
..x..0..x..4..x....x..4..x..6..x....x..1..x..6..x....x..0..x..6..x
..1..x..3..x..7....0..x..1..x..9....0..x..2..x..3....3..x..4..x..9
..x..2..x..5..x....x..5..x..8..x....x..7..x..8..x....x..1..x..7..x
..8..x..9..x.10....2..x..3..x.10....4..x..5..x.11....5..x..8..x.11
..x..6..x.11..x....x..7..x.11..x....x..9..x.10..x....x..2..x.10..x
A215294
Number of permutations of 0..floor((n*3-2)/2) on odd squares of an n X 3 array such that each row and column of odd squares is increasing.
Original entry on oeis.org
1, 3, 6, 30, 70, 420, 1050, 6930, 18018, 126126, 336336, 2450448, 6651216, 49884120, 137181330, 1051723530, 2921454250, 22787343150, 63804560820, 504636071940, 1422156202740, 11377249621920, 32235540595440, 260363981732400
Offset: 1
Some solutions for n=5:
x 1 x x 0 x x 0 x x 4 x x 0 x x 1 x x 1 x
0 x 5 2 x 4 2 x 5 0 x 2 1 x 2 0 x 5 0 x 3
x 3 x x 1 x x 1 x x 5 x x 3 x x 2 x x 2 x
2 x 6 3 x 6 3 x 6 1 x 3 4 x 6 3 x 6 4 x 5
x 4 x x 5 x x 4 x x 6 x x 5 x x 4 x x 6 x
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a := n -> `if`(irem(n, 2) = 0, ((1/2)*n+1)*factorial((3/2)*n)/ (factorial((1/2)*n+1)^2*factorial((1/2)*n)), factorial((3/2)*n+3/2)/ (factorial((1/2)*n+1/2)^3*((9/2)*n+3/2))): # Peter Luschny, Sep 30 2018
A215295
Number of permutations of 0..floor((n*5-2)/2) on odd squares of an nX5 array such that each row and column of odd squares is increasing.
Original entry on oeis.org
1, 10, 70, 2100, 23100, 1051050, 14294280, 814773960, 12547518984, 824551247520, 13781785137120, 999179422441200, 17699749768958400, 1379105502831342000, 25513451802379827000, 2100607531729272423000, 40191624107086745693400
Offset: 1
Some solutions for n=5
..x..2..x..6..x....x..1..x..5..x....x..0..x..5..x....x..0..x..2..x
..0..x..3..x..4....0..x..2..x..7....2..x..4..x.10....3..x..6..x..8
..x..5..x.10..x....x..3..x..9..x....x..1..x..8..x....x..1..x..7..x
..1..x..7..x..8....4..x..6..x.11....6..x..7..x.11....4..x..9..x.11
..x..9..x.11..x....x..8..x.10..x....x..3..x..9..x....x..5..x.10..x
A215296
Number of permutations of 0..floor((n*7-2)/2) on odd squares of an nX7 array such that each row and column of odd squares is increasing.
Original entry on oeis.org
1, 35, 1050, 210210, 14294280, 5703417720, 577185873264, 337653735859440, 43364386933948080, 32436561426593163840, 4886336289191784467040, 4340695403565368534887200, 733267473530864041786302000
Offset: 1
Some solutions for n=3
..x..0..x..1..x..3..x....x..0..x..2..x..5..x....x..0..x..1..x..3..x
..2..x..4..x..6..x..9....3..x..6..x..8..x..9....5..x..6..x..8..x..9
..x..5..x..7..x..8..x....x..1..x..4..x..7..x....x..2..x..4..x..7..x
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