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A266470
T(n,k) = number of n X k binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
12
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 29 2015
STATUS
approved