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T(n,k)=number of nXk binary matrices with rows and then columns in strictly increasing order as binary numbers
6

%I #3 Mar 31 2012 12:35:49

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,19,6,

%T 0,0,0,0,0,0,0,196,4,0,0,0,0,0,0,0,721,873,1,0,0,0,0,0,0,0,0,17630,

%U 2200,0,0,0,0,0,0,0,0,0,67264,194176,3489,0,0,0,0,0,0,0,0,0,0,3673129,1283875

%N T(n,k)=number of nXk binary matrices with rows and then columns in strictly increasing order as binary numbers

%C Table starts

%C .0.0.0....0.........0...............0.....................0

%C .0.0.0....0.........0...............0.....................0

%C .0.0.0....0.........0...............0.....................0

%C .0.0.1....0.........0...............0.....................0

%C .0.0.4...19.........0...............0.....................0

%C .0.0.6..196.......721...............0.....................0

%C .0.0.4..873.....17630...........67264.....................0

%C .0.0.1.2200....194176.........3673129..............16731459

%C .0.0.0.3489...1283875........91610331............1986193307

%C .0.0.0.3675...5754681......1408620622..........106664349231

%C .0.0.0.2646..18841145.....15031688395.........3595756291357

%C .0.0.0.1319..47481210....119897184624........85146473995739

%C .0.0.0..454..95722629....754355167375......1517858668914081

%C .0.0.0..105.158918058...3897928580882.....21458940104760027

%C .0.0.0...15.222078101..17056422818565....250470869515416956

%C .0.0.0....1.265522138..64708241443623...2489728914680959379

%C .0.0.0....0.274798153.216764641206495..21589512131961793054

%C .0.0.0....0.248033249.650403229942940.166424857870089951949

%H R. H. Hardin, <a href="/A180989/b180989.txt">Table of n, a(n) for n=1..365</a>

%e All solutions for 5X4

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

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

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

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

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

%e ...

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

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

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

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

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

%e ...

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

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

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

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

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

%e ...

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

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

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

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

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

%K nonn,tabl

%O 1,26

%A _R. H. Hardin_ Sep 30 2010