A212943 T(n,k)=Number of nXk 0..k-1 arrays with no column j greater than or equal to than column j-1 in all rows

1, 1, 1, 1, 7, 1, 1, 181, 37, 1, 1, 10311, 9019, 175, 1, 1, 1016501, 6470341, 331489, 781, 1, 1, 152747323, 10058484751, 2509306671, 10669771, 3367, 1, 1, 32383630189, 28744943858947, 52311221188001, 801439905901, 320396041, 14197, 1, 1

Offset

1,5

Comments

Table starts

.1...1........1............1..................1........................1

.1...7......181........10311............1016501................152747323

.1..37.....9019......6470341........10058484751...........28744943858947

.1.175...331489...2509306671.....52311221188001......2438624218076957695

.1.781.10669771.801439905901.212180664326328751.153322267564381742818531

Links

R. H. Hardin, Table of n, a(n) for n = 1..191

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 7*a(n-1) -12*a(n-2)

k=3: a(n) = 55*a(n-1) -936*a(n-2) +4860*a(n-3)

k=4: a(n) = 631*a(n-1) -144700*a(n-2) +15035200*a(n-3) -702208000*a(n-4) +11468800000*a(n-5)

The coefficient of a(n-1) is A209668(k) (through at least k=1..7)

Example

Some solutions for n=4 k=4
..1..3..2..2....0..0..0..3....1..3..0..1....1..3..2..1....1..3..3..3
..1..1..2..2....0..1..1..2....0..0..1..0....1..1..0..3....2..3..0..3
..0..1..3..1....0..2..2..1....0..1..1..3....2..3..3..0....0..2..0..2
..3..1..0..3....2..1..0..2....3..0..3..1....1..0..3..0....2..0..1..0

Crossrefs

Column 2 is A005061

cf. A212930

Sequence in context: A188644 A331899 A111830 * A174588 A366316 A199001

Adjacent sequences: A212940 A212941 A212942 * A212944 A212945 A212946

Keyword

nonn,tabl

Author

R. H. Hardin May 31 2012

Status

approved