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.

1, 2, 6, 280, 23100, 85765680, 577185873264, 346915095471584640, 381134230556959188429120, 62144711688730139887005809020800, 18592619468814454675301397184588597886400

Offset

1,2

Links

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

Formula

f1=floor(n/2),

f2=floor((n+1)/2),

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

Example

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

Crossrefs

Diagonal of A215297.

Sequence in context: A007190 A164829 A028337 * A264410 A135014 A321571

Adjacent sequences: A215290 A215291 A215292 * A215294 A215295 A215296

Keyword

nonn

Author

R. H. Hardin, Aug 07 2012

Status

approved