A267245 T(n,k)=Number of nXk binary arrays with row sums nondecreasing and columns lexicographically nondecreasing.

2, 3, 3, 4, 7, 4, 5, 13, 15, 5, 6, 22, 42, 31, 6, 7, 34, 105, 141, 63, 7, 8, 50, 232, 567, 486, 127, 8, 9, 70, 475, 1986, 3351, 1685, 255, 9, 10, 95, 904, 6292, 20040, 20676, 5804, 511, 10, 11, 125, 1632, 18205, 107015, 220235, 129129, 19769, 1023, 11, 12, 161, 2806

Offset

1,1

Comments

Table starts

..2....3......4........5..........6............7..............8

..3....7.....13.......22.........34...........50.............70

..4...15.....42......105........232..........475............904

..5...31....141......567.......1986.........6292..........18205

..6...63....486.....3351......20040.......107015.........516084

..7..127...1685....20676.....220235......2093467.......17892539

..8..255...5804...129129....2499080.....43555569......683027146

..9..511..19769...804817...28501471....924051709....27044976947

.10.1023..66544..4982759..323067002..19614050515..1079112886476

.11.2047.221581.30629206.3626695952.413556580944.42860145907558

Links

R. H. Hardin, Table of n, a(n) for n = 1..216

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -2*a(n-2)

k=3: a(n) = 10*a(n-1) -39*a(n-2) +76*a(n-3) -79*a(n-4) +42*a(n-5) -9*a(n-6)

k=4: [order 10]

k=5: [order 14]

k=6: [order 22]

k=7: [order 32]

Empirical for row n:

n=1: a(n) = 2*a(n-1) -a(n-2)

n=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)

n=3: [order 13]

Example

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

Crossrefs

Column 1 and row 1 are A000027(n+1).

Column 2 is A000225(n+1).

Row 2 is A002623.

Row 3 is A233302(n-1).

Row 4 is A233303(n-1).

Sequence in context: A241956 A227125 A248944 * A266428 A180985 A227385

Adjacent sequences: A267242 A267243 A267244 * A267246 A267247 A267248

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 12 2016

Status

approved