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

Author

R. H. Hardin, Aug 07 2012

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 4 of A215292.

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).