A264557 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 3.

1, 1, 1, 2, 4, 8, 24, 72, 216, 864, 3456, 13824, 69120, 345600, 1728000, 10368000, 62208000, 373248000, 2612736000, 18289152000, 128024064000, 1024192512000, 8193540096000, 65548320768000, 589934886912000, 5309413982208000, 47784725839872000

Offset: 1

Author

R. H. Hardin, Nov 17 2015

Keywords

• nonn

Comments

Column 1 of A264560.

Examples

			All solutions for n=4
..0....3
..3....0
..1....1
..2....2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..48

Crossrefs

Cf. A264560.

Column k=3 of A275062.

Programs

Mathematica

Table[Product[Floor[(n + i)/3]!, {i, 0, 2}], {n, 1, 30}] (* Vaclav Kotesovec, Oct 02 2018 *)

Formula

a(n) = Product_{i=0..2} ceiling((n-i)/3)!. - Alois P. Heinz, Jul 09 2016

a(n) ~ 2 * Pi * (n+1)! / 3^(n + 3/2). - Vaclav Kotesovec, Oct 02 2018