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

1,5

Links

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

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

Example

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

Mathematica

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

Crossrefs

Column 1 of A264638.

Column k=4 of A275062.

Sequence in context: A027155 A379335 A129335 * A046237 A013084 A263535

Adjacent sequences: A264632 A264633 A264634 * A264636 A264637 A264638

Keyword

nonn

Author

R. H. Hardin, Nov 19 2015

Status

approved