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%I #6 Dec 27 2023 17:31:14
%S 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,
%T 39,137,232,147,42,9,2,10,52,261,735,794,303,59,10,2,11,67,463,2090,
%U 4074,2574,590,80,11,2,12,84,775,5371,18808,22128,7797,1090,106,12,2,13,103
%N T(n,k) = number of n X k binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
%C Table starts
%C ..2...2....2.....2.......2.........2..........2............2.............2
%C ..3...4....5.....6.......7.........8..........9...........10............11
%C ..4...7...12....19......28........39.........52...........67............84
%C ..5..12...29....66.....137.......261........463..........775..........1237
%C ..6..19...67...232.....735......2090.......5371........12645.........27639
%C ..7..29..147...794....4074.....18808......77320.......285494........959672
%C ..8..42..303..2574...22128....175180....1231170......7652503......42460424
%C ..9..59..590..7797..113677...1595005...20115063....223521350....2195862381
%C .10..80.1090.22058..544142..13720886..319006954...6568208183..119000455681
%C .11.106.1922.58469.2417707.109830369.4768598707.185724489849.6373048347212
%H R. H. Hardin, <a href="/A266470/b266470.txt">Table of n, a(n) for n = 1..163</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-2)
%F k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)
%F k=3: [order 12]
%F Empirical for row n:
%F n=1: a(n) = 2
%F n=2: a(n) = n + 2
%F n=3: a(n) = n^2 + 3
%F n=4: [polynomial of degree 5]
%F n=5: [polynomial of degree 9]
%F n=6: [polynomial of degree 19]
%F n=7: [polynomial of degree 34]
%e Some solutions for n=4 k=4
%e ..0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..1
%e ..0..0..0..1....0..0..1..0....0..0..0..1....0..0..1..1....0..0..1..0
%e ..0..1..1..0....1..1..0..0....1..1..1..0....1..1..0..0....1..1..0..0
%e ..1..0..0..0....1..1..1..0....1..1..1..1....1..1..1..1....1..1..0..0
%Y Column 1 is A000027(n+1).
%Y Row 2 is A000027(n+2).
%Y Row 3 is A117950.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 29 2015
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