A212930 T(n,k)=Number of nXk 0..k-1 arrays with no column j greater than column j-1 in all rows

1, 3, 1, 10, 15, 1, 35, 568, 63, 1, 126, 39695, 18226, 255, 1, 462, 4431876, 14177855, 518320, 1023, 1, 1716, 724082352, 23124921876, 4041974015, 14230810, 4095, 1, 6435, 163050236504, 68264066143602, 85800824609376, 1075113010175, 386357608

Offset

1,2

Comments

Table starts

.1....3.......10............35................126......................462

.1...15......568.........39695............4431876................724082352

.1...63....18226......14177855........23124921876...........68264066143602

.1..255...518320....4041974015.....85800824609376......4051316109991426752

.1.1023.14230810.1075113010175.285912852294921876.207406617181155352354002

Links

R. H. Hardin, Table of n, a(n) for n = 1..172

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-1) -4*a(n-2)

k=3: a(n) = 37*a(n-1) -279*a(n-2) +243*a(n-3)

k=4: a(n) = 405*a(n-1) -43860*a(n-2) +1524160*a(n-3) -15636480*a(n-4) +14155776*a(n-5)

The coefficient of a(n-1) is A209671(k) (through at least k=1..7)

Example

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

Crossrefs

Column 2 is A024036

Row 1 is A001700(n-1)

cf. A212943

Sequence in context: A064060 A176740 A134991 * A225725 A095327 A225753

Adjacent sequences: A212927 A212928 A212929 * A212931 A212932 A212933

Keyword

nonn,tabl

Author

R. H. Hardin May 31 2012

Status

approved