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T(n,k)=number of nXk binary matrices with floor((n*k)/2) 1's and rows and columns in lexicographically nondecreasing order
2

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

%S 1,1,1,1,3,1,1,4,4,1,1,7,10,7,1,1,9,27,27,9,1,1,13,58,121,58,13,1,1,

%T 16,122,483,483,122,16,1,1,21,238,1751,3680,1751,238,21,1,1,25,433,

%U 5694,24779,24779,5694,433,25,1,1,31,737,16870,152453,326650,152453,16870,737

%N T(n,k)=number of nXk binary matrices with floor((n*k)/2) 1's and rows and columns in lexicographically nondecreasing order

%C Table starts

%C .1..1....1......1........1..........1............1..............1

%C .1..3....4......7........9.........13...........16.............21

%C .1..4...10.....27.......58........122..........238............433

%C .1..7...27....121......483.......1751.........5694..........16870

%C .1..9...58....483.....3680......24779.......152453.........804538

%C .1.13..122...1751....24779.....326650......3826202.......39589830

%C .1.16..238...5694...152453....3826202.....91271990.....1819250859

%C .1.21..433..16870...804538...39589830...1819250859....74872992399

%C .1.25..737..46014..3969107..364013320..34112520431..2730227923892

%C .1.31.1208.116842.17135660.3005372641.534428405524.88478723671041

%H R. H. Hardin, <a href="/A180979/b180979.txt">Table of n, a(n) for n=1..220</a>

%e All solutions for 3X4

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

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

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

%e ...

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

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

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

%e ...

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

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

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

%e ...

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

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

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

%e ...

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

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

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

%e ...

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_ Sep 30 2010