A215286 Number of permutations of 0..floor((n*n-1)/2) on even squares of an n X n array such that each row and column of even squares is increasing.

1, 2, 10, 280, 60060, 85765680, 2061378118800, 346915095471584640, 1736278161426147413954880, 62144711688730139887005809020800, 103104526145243794108489566205445861006400

Offset: 1

Author

R. H. Hardin, Aug 07 2012

Keywords

• nonn

Comments

Diagonal of A215292.

Examples

			Some solutions for n=5
..0..x..1..x..2....0..x..2..x..6....0..x..2..x..4....1..x..2..x..6
..x..4..x..7..x....x..1..x..3..x....x..3..x..5..x....x..0..x..8..x
..3..x..6..x..9....5..x..8..x.11....1..x..8..x..9....3..x..5..x.10
..x..5..x.11..x....x..4..x..9..x....x..7..x.10..x....x..9..x.12..x
..8..x.10..x.12....7..x.10..x.12....6..x.11..x.12....4..x..7..x.11
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A060854, A215292.

Formula

f1 = floor((n+1)/2)

f2 = floor(n/2)

T(n,k) = A060854(f1,f1)*A060854(f2,f2)*binomial(f1*f1+f2*f2,f1*f1).