%I #5 Mar 31 2012 12:35:51
%S 1,2,2,2,5,2,3,8,8,3,3,15,22,15,3,4,21,75,75,21,4,4,34,152,380,152,34,
%T 4,5,44,410,1518,1518,410,44,5,5,65,719,6450,11499,6450,719,65,5,6,80,
%U 1632,20066,98343,98343,20066,1632,80,6,6,111,2564,69431,556989,1497764
%N T(n,k)=Number of nXk binary arrays with each sum of a(1..i,1..j) no greater than i*j/2 and rows and columns in nondecreasing order
%C Table starts
%C .1...2....2......3........3...........4............4............5............5
%C .2...5....8.....15.......21..........34...........44...........65...........80
%C .2...8...22.....75......152.........410..........719.........1632.........2564
%C .3..15...75....380.....1518........6450........20066........69431.......178672
%C .3..21..152...1518....11499.......98343.......556989......3662106.....16124119
%C .4..34..410...6450....98343.....1497764.....17507704....208323889...1832450809
%C .4..44..719..20066...556989....17507704....408834576..10087837825.175291717602
%C .5..65.1632..69431..3662106...208323889..10087837825.475512062908
%C .5..80.2564.178672.16124119..1832450809.175291717602
%C .6.111.5130.525241.85225430.17253002617
%H R. H. Hardin, <a href="/A183413/b183413.txt">Table of n, a(n) for n = 1..144</a>
%e Some solutions for 5X4
%e ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1
%e ..0..0..1..0....0..0..0..1....0..0..0..1....0..0..1..0....0..0..1..1
%e ..0..0..1..1....0..0..0..1....0..0..1..1....0..0..1..0....0..1..0..0
%e ..0..1..0..0....0..1..1..0....0..1..0..0....0..1..0..0....1..0..1..0
%e ..0..1..1..1....1..0..0..1....0..1..0..0....1..0..0..0....1..1..0..1
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Jan 04 2011
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