A266470 T(n,k) = number of n X k binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.

2, 2, 3, 2, 4, 4, 2, 5, 7, 5, 2, 6, 12, 12, 6, 2, 7, 19, 29, 19, 7, 2, 8, 28, 66, 67, 29, 8, 2, 9, 39, 137, 232, 147, 42, 9, 2, 10, 52, 261, 735, 794, 303, 59, 10, 2, 11, 67, 463, 2090, 4074, 2574, 590, 80, 11, 2, 12, 84, 775, 5371, 18808, 22128, 7797, 1090, 106, 12, 2, 13, 103

Offset: 1

Author

R. H. Hardin, Dec 29 2015

Keywords

• nonn
• tabl

Comments

Table starts

..2...2....2.....2.......2.........2..........2............2.............2

..3...4....5.....6.......7.........8..........9...........10............11

..4...7...12....19......28........39.........52...........67............84

..5..12...29....66.....137.......261........463..........775..........1237

..6..19...67...232.....735......2090.......5371........12645.........27639

..7..29..147...794....4074.....18808......77320.......285494........959672

..8..42..303..2574...22128....175180....1231170......7652503......42460424

..9..59..590..7797..113677...1595005...20115063....223521350....2195862381

.10..80.1090.22058..544142..13720886..319006954...6568208183..119000455681

.11.106.1922.58469.2417707.109830369.4768598707.185724489849.6373048347212

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..163

Crossrefs

Column 1 is A000027(n+1).

Row 2 is A000027(n+2).

Row 3 is A117950.

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) -2*a(n-3) +3*a(n-4) -a(n-5)

k=3: [order 12]

Empirical for row n:

n=1: a(n) = 2

n=2: a(n) = n + 2

n=3: a(n) = n^2 + 3

n=4: [polynomial of degree 5]

n=5: [polynomial of degree 9]

n=6: [polynomial of degree 19]

n=7: [polynomial of degree 34]