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T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with the (lower) median of each row and column nondecreasing
3

%I #4 Feb 09 2014 06:09:36

%S 3470,53831,53831,845952,3203193,845952,11887072,143951490,143951490,

%T 11887072,179403984,7420279118,30191128785,7420279118,179403984,

%U 2431745813,324957818406,4507667952676,4507667952676,324957818406

%N T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with the (lower) median of each row and column nondecreasing

%C Table starts

%C .......3470........53831........845952......11887072.......179403984

%C ......53831......3203193.....143951490....7420279118....324957818406

%C .....845952....143951490...30191128785.4507667952676.915350182586052

%C ...11887072...7420279118.4507667952676

%C ..179403984.324957818406

%C .2431745813

%H R. H. Hardin, <a href="/A237548/b237548.txt">Table of n, a(n) for n = 1..24</a>

%e Some solutions for n=1 k=1

%e ..2..0..1....0..1..2....1..1..2....2..0..1....0..1..2....1..0..2....1..0..1

%e ..0..1..1....1..2..0....1..0..2....0..1..1....1..1..2....1..2..1....1..2..1

%e ..0..1..1....0..1..1....1..2..0....1..2..2....2..0..1....1..1..1....0..1..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 09 2014