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

1,2

Comments

Diagonal of A215292.

Links

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

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).

Example

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

Crossrefs

Cf. A060854, A215292.

Sequence in context: A074056 A206158 A144288 * A260231 A003047 A028580

Adjacent sequences: A215283 A215284 A215285 * A215287 A215288 A215289

Keyword

nonn

Author

R. H. Hardin, Aug 07 2012

Status

approved