A264635 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.

1, 1, 1, 1, 2, 4, 8, 16, 48, 144, 432, 1296, 5184, 20736, 82944, 331776, 1658880, 8294400, 41472000, 207360000, 1244160000, 7464960000, 44789760000, 268738560000, 1881169920000, 13168189440000, 92177326080000, 645241282560000, 5161930260480000

Offset: 1

Author

R. H. Hardin, Nov 19 2015

Keywords

• nonn

Examples

			All solutions for n=6:
  0    4    4    0
  4    0    0    4
  1    1    5    5
  5    5    1    1
  2    2    2    2
  3    3    3    3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..62

Crossrefs

Column 1 of A264638.

Column k=4 of A275062.

Programs

Mathematica

Table[Product[Floor[(n + i)/4]!, {i, 0, 3}], {n, 1, 30}] (* Vaclav Kotesovec, Oct 02 2018 *)

Formula

a(n) = Product_{i=0..3} floor((n+i)/4)!. - Alois P. Heinz, Jul 12 2016

a(n) ~ Pi^(3/2) * n^(3/2) * n! / 2^(2*n + 5/2). - Vaclav Kotesovec, Oct 02 2018

Sum_{n>0} floor((n-1)/4)/a(n) = 1. - Peter McNair, May 29 2022