A215288 Number of permutations of 0..floor((n*4-1)/2) on even squares of an n X 4 array such that each row and column of even squares is increasing.

1, 6, 30, 280, 2100, 23100, 210210, 2522520, 25729704, 325909584, 3585005424, 47117214144, 546896235600, 7383099180600, 89212448432250, 1229149289511000, 15323394475903800, 214527522662653200, 2742051789669912720

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

f3=floor((n+1)/2),

f4=floor(n/2),

a(n) = A060854(2,f3)*A060854(2,f4)*binomial(2*f3+2*f4,2*f3).

Example

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

Crossrefs

Column 4 of A215292.

Sequence in context: A099031 A066108 A205339 * A295611 A264641 A360824

Adjacent sequences: A215285 A215286 A215287 * A215289 A215290 A215291

Keyword

nonn

Author

R. H. Hardin, Aug 07 2012

Status

approved