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T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with the (lower) medians of each row equal and of each column equal
6

%I #4 Feb 12 2014 09:31:43

%S 68,290,290,1412,7552,1412,5708,39842,39842,5708,25832,938176,608372,

%T 938176,25832,103538,5871266,12331252,12331252,5871266,103538,447332,

%U 119520256,213982232,1727378144,213982232,119520256,447332,1790084

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with the (lower) medians of each row equal and of each column equal

%C Table starts

%C .......68...........290............1412...............5708..............25832

%C ......290..........7552...........39842.............938176............5871266

%C .....1412.........39842..........608372...........12331252..........213982232

%C .....5708........938176........12331252.........1727378144........27738515408

%C ....25832.......5871266.......213982232........27738515408......1405996950752

%C ...103538.....119520256......3813889762......3276185440256....135526127886578

%C ...447332.....847692866.....67892256692.....62580997848692...8101710521927192

%C ..1790084...15310585024...1145451277532...6267389933189344.662870061789157280

%C ..7524728..118493356610..20262099994952.137204103504548368

%C .30101684.1955650250944.333280098908492

%H R. H. Hardin, <a href="/A237745/b237745.txt">Table of n, a(n) for n = 1..83</a>

%e Some solutions for n=2 k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 12 2014