%I #4 Jan 11 2014 13:27:34
%S 16,58,58,209,382,209,746,2501,2501,746,2660,16117,29533,16117,2660,
%T 9476,103736,343063,343063,103736,9476,33753,666171,3977050,7186597,
%U 3977050,666171,33753,120216,4277473,45985647,150092214,150092214,45985647
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the sum of each 2X2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise
%C Table starts
%C ......16.........58..........209.............746...............2660
%C ......58........382.........2501...........16117.............103736
%C .....209.......2501........29533..........343063............3977050
%C .....746......16117.......343063.........7186597..........150092214
%C ....2660.....103736......3977050.......150092214.........5645191775
%C ....9476.....666171.....45985647......3125826729.......211711499238
%C ...33753....4277473....531586422.....65064307612......7934494535832
%C ..120216...27457539...6142770286...1353709346996....297222406479878
%C ..428160..176252122..70981491138..28162807605171..11132550506229506
%C .1524918.1131335938.820170288679.585865208407308.416940408877849294
%H R. H. Hardin, <a href="/A235517/b235517.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -6*a(n-3) +a(n-4) +2*a(n-5)
%F k=2: [order 13]
%F k=3: [order 43]
%e Some solutions for n=3 k=4
%e ..0..0..0..0..0....0..0..1..0..0....0..0..0..1..0....0..0..0..1..0
%e ..0..0..1..0..1....0..1..1..1..1....1..0..1..1..0....0..0..1..1..1
%e ..1..1..0..0..0....1..1..0..1..0....1..0..0..1..0....1..1..0..1..0
%e ..1..0..1..0..1....1..0..1..0..0....1..1..1..1..0....1..0..1..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 11 2014
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