A264791 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 7.

1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 384, 1152, 3456, 10368, 31104, 93312, 279936, 1119744, 4478976, 17915904, 71663616, 286654464, 1146617856, 4586471424, 22932357120, 114661785600, 573308928000, 2866544640000, 14332723200000, 71663616000000

Offset

1,8

Comments

Column 1 of A264794.

Links

R. H. Hardin, Table of n, a(n) for n = 1..91

Formula

a(n) = Product_{i=0..6} floor((n+i)/7)!. - Alois P. Heinz, Jul 12 2016

a(n) ~ (2*Pi*n)^3 * n! / 7^(n + 7/2). - Vaclav Kotesovec, Oct 02 2018

Example

All solutions for n=11
..0....0....7....0....7....0....7....7....7....7....0....0....0....7....0....7
..7....7....0....7....0....7....0....0....0....0....7....7....7....0....7....0
..1....1....8....8....8....1....1....8....1....8....8....8....8....1....1....1
..8....8....1....1....1....8....8....1....8....1....1....1....1....8....8....8
..9....2....2....9....9....2....9....2....2....9....9....2....2....9....9....2
..2....9....9....2....2....9....2....9....9....2....2....9....9....2....2....9
..3....3...10....3....3...10...10....3...10...10...10...10....3....3...10....3
.10...10....3...10...10....3....3...10....3....3....3....3...10...10....3...10
..4....4....4....4....4....4....4....4....4....4....4....4....4....4....4....4
..5....5....5....5....5....5....5....5....5....5....5....5....5....5....5....5
..6....6....6....6....6....6....6....6....6....6....6....6....6....6....6....6

Mathematica

Table[Product[Floor[(n + i)/7]!, {i, 0, 6}], {n, 1, 40}] (* Vaclav Kotesovec, Oct 02 2018 *)

Crossrefs

Cf. A264794.

Column k=7 of A275062.

Sequence in context: A275074 A290687 A290855 * A290851 A290670 A079838

Adjacent sequences: A264788 A264789 A264790 * A264792 A264793 A264794

Keyword

nonn

Author

R. H. Hardin, Nov 25 2015

Status

approved