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%I #4 Jan 06 2016 11:32:01
%S 2,2,3,2,4,4,2,4,7,5,2,5,9,12,6,2,5,12,20,19,7,2,6,14,35,44,29,8,2,6,
%T 19,52,100,92,42,9,2,7,21,82,210,288,182,59,10,2,7,26,115,429,871,794,
%U 340,80,11,2,8,30,169,816,2577,3566,2077,605,106,12,2,8,35,232,1534,7185
%N T(n,k)=Number of nXk binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.
%C Table starts
%C ..2...2....2.....2......2.......2........2..........2.........2.........2
%C ..3...4....4.....5......5.......6........6..........7.........7.........8
%C ..4...7....9....12.....14......19.......21.........26........30........35
%C ..5..12...20....35.....52......82......115........169.......232.......322
%C ..6..19...44...100....210.....429......816.......1534......2727......4753
%C ..7..29...92...288....871....2577.....7185......19529.....50216....125786
%C ..8..42..182...794...3566...15850....68890.....288333...1155281...4410923
%C ..9..59..340..2077..13899...96503...671796....4605960..30319512.191420936
%C .10..80..605..5110..50841..555060..6347005...73046059.821453747
%C .11.106.1028.11869.173470.2977370.56180274.1104862960
%H R. H. Hardin, <a href="/A266935/b266935.txt">Table of n, a(n) for n = 1..160</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-2)
%F k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)
%F k=3: [order 11]
%F k=4: [order 31]
%F Empirical for row n:
%F n=1: a(n) = a(n-1)
%F n=2: a(n) = a(n-1) +a(n-2) -a(n-3)
%F n=3: a(n) = a(n-1) +a(n-2) -a(n-4) -a(n-5) +a(n-6)
%F n=4: [order 17]
%e Some solutions for n=4 k=4
%e ..0..0..0..1....0..0..1..1....0..0..0..1....0..0..0..0....0..0..1..1
%e ..0..1..1..0....1..1..0..0....1..1..1..0....0..0..0..0....1..1..0..0
%e ..1..0..0..1....1..1..1..1....1..1..1..1....0..0..0..1....1..1..0..0
%e ..1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..1..1
%Y Column 1 is A000027(n+1).
%Y Column 2 is A266464.
%Y Row 2 is A004526(n+6).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 06 2016
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