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%I #18 Dec 21 2020 18:05:39
%S 1,1,1,1,2,1,1,2,2,1,1,3,3,3,1,1,3,5,5,3,1,1,4,6,8,6,4,1,1,4,8,12,12,
%T 8,4,1,1,5,10,18,20,18,10,5,1,1,5,13,24,32,32,24,13,5,1,1,6,15,33,49,
%U 58,49,33,15,6,1,1,6,18,43,73,94,94,73,43,18,6,1,1,7,21,55,102,151,169,151,102,55,21,7,1
%N T(n,k) is the number of n X k binary matrices with floor((n*k)/2) 1's and rows in lexicographically nondecreasing order and columns in lexicographically nonincreasing order.
%C T(n,k) is the cardinality of a maximal antichain in the partially ordered set consisting of all k-tuples of natural numbers (x_1,...,x_k) with 0 < x_1 < ... < x_k < n+2, with the componentwise ordering, (x_1,...,x_k) <= (y_1,...,y_k) if and only if x_1 <= y_1, ..., x_k <= y_k. - _Mamuka Jibladze_, Nov 15 2020
%H R. H. Hardin, <a href="/A180980/b180980.txt">Table of n, a(n) for n=1..363</a>
%e Table starts:
%e 1.1..1..1...1...1...1....1....1....1....1.....1.....1.....1.....1......1
%e 1.2..2..3...3...4...4....5....5....6....6.....7.....7.....8.....8......9
%e 1.2..3..5...6...8..10...13...15...18...21....25....28....32....36.....41
%e 1.3..5..8..12..18..24...33...43...55...69....86...104...126...150....177
%e 1.3..6.12..20..32..49...73..102..141..190...252...325...414...521....649
%e 1.4..8.18..32..58..94..151..227..338..480...676...920..1242..1636...2137
%e 1.4.10.24..49..94.169..289..468..734.1117..1656..2385..3370..4672...6375
%e 1.5.13.33..73.151.289..526..910.1514.2430..3788..5744..8512.12346..17575
%e 1.5.15.43.102.227.468..910.1667.2934.4968..8150.12954.20094.30441..45207
%e 1.6.18.55.141.338.734.1514.2934.5448.9686.16660.27718.44916.70922.109583
%e All solutions for 3 X 4:
%e 0..0..0..0....0..0..0..0....1..0..0..0....1..0..0..0....1..1..0..0
%e 1..1..1..0....1..1..0..0....1..0..0..0....1..1..0..0....1..1..0..0
%e 1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..0..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Sep 30 2010
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