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

1,4

Comments

Column 1 of A264560.

Links

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

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

Example

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

Mathematica

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

Crossrefs

Cf. A264560.

Column k=3 of A275062.

Sequence in context: A264570 A115115 A026097 * A067646 A152875 A179190

Adjacent sequences: A264554 A264555 A264556 * A264558 A264559 A264560

Keyword

nonn

Author

R. H. Hardin, Nov 17 2015

Status

approved