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

Author

R. H. Hardin, Jan 12 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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).

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]