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%I #10 Jan 10 2019 10:23:37
%S 2,4,9,20,44,92,182,340,605,1028,1680,2651,4058,6045,8793,12518,17484,
%T 24001,32438,43222,56853,73901,95024,120965,152570,190786,236681,
%U 291440,356388,432986,522854,627768,749685,890738,1053264,1239799,1453106
%N Number of n X 3 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.
%H R. H. Hardin, <a href="/A266930/b266930.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - 3*a(n-3) + 6*a(n-4) - 6*a(n-7) + 3*a(n-8) + 4*a(n-9) - 4*a(n-10) + a(n-11).
%F Empirical g.f.: x*(2 - 4*x + x^2 + 6*x^3 - x^5 - 4*x^6 + 4*x^7 + 3*x^8 - 4*x^9 + x^10) / ((1 - x)^7*(1 + x)^2*(1 + x + x^2)). - _Colin Barker_, Jan 10 2019.
%e Some solutions for n=4:
%e ..0..0..1....0..0..0....0..0..0....0..0..0....0..1..1....0..0..0....0..0..1
%e ..0..1..0....0..0..1....0..0..0....0..0..0....1..0..1....0..0..1....0..0..1
%e ..1..0..0....1..1..0....0..0..0....1..1..1....1..1..0....0..1..0....1..1..0
%e ..1..1..1....1..1..0....1..1..1....1..1..1....1..1..0....1..0..0....1..1..0
%Y Column 3 of A266935.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 06 2016
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