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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000027(n+1).

Row 2 is A000027(n+2).

Row 3 is A117950.

Sequence in context: A266935 A175012 A051693 * A371745 A209700 A115980

Adjacent sequences: A266467 A266468 A266469 * A266471 A266472 A266473

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 29 2015

Status

approved