A264701 Number of n X 1 arrays of permutations of 0..n-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 6.

1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 192, 576, 1728, 5184, 15552, 46656, 186624, 746496, 2985984, 11943936, 47775744, 191102976, 955514880, 4777574400, 23887872000, 119439360000, 597196800000, 2985984000000, 17915904000000, 107495424000000, 644972544000000

Offset

1,7

Comments

Column 1 of A264704.

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

a(n) = Product_{i=0..5} floor((n+i)/6)!. - Alois P. Heinz, Jul 12 2016

a(n) ~ (2*Pi*n)^(5/2) * n! / 6^(n + 3). - Vaclav Kotesovec, Oct 02 2018

Example

All solutions for n=8
..6....6....0....0
..0....0....6....6
..7....1....1....7
..1....7....7....1
..2....2....2....2
..3....3....3....3
..4....4....4....4
..5....5....5....5

Mathematica

Table[Product[Floor[(n + i)/6]!, {i, 0, 5}], {n, 1, 40}] (* Vaclav Kotesovec, Oct 02 2018 *)

Crossrefs

Cf. A264704.

Column k=6 of A275062.

Sequence in context: A180209 A344493 A275073 * A195904 A101333 A367652

Adjacent sequences: A264698 A264699 A264700 * A264702 A264703 A264704

Keyword

nonn

Author

R. H. Hardin, Nov 21 2015

Status

approved