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%I #20 Mar 29 2018 05:30:52
%S 2,5,8,15,21,34,44,65,80,111,132,175,203,260,296,369,414,505,560,671,
%T 737,870,948,1105,1196,1379,1484,1695,1815,2056,2192,2465,2618,2925,
%U 3096,3439,3629,4010,4220,4641,4872,5335,5588,6095,6371,6924,7224,7825,8150
%N Number of n X 2 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 Column 2 of A183413.
%H R. H. Hardin, <a href="/A183409/b183409.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).
%F Conjecture: a(n) = (2*n^3+11*n^2+31*n+27+(n^2+n+5)*(-1)^n)/32. - _Luce ETIENNE_, Nov 18 2014
%F Empirical g.f.: x*(2 + 3*x - 3*x^2 - 2*x^3 + 3*x^4 + x^5 - x^6) / ((1 - x)^4*(1 + x)^3). - _Colin Barker_, Mar 29 2018
%e Some solutions for 4 X 2:
%e ..0..0....0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..0....0..1
%e ..0..0....0..1....0..0....0..1....0..0....0..1....0..1....0..1....0..0....0..1
%e ..0..0....1..0....0..0....0..1....0..1....0..1....1..0....1..0....0..1....0..1
%e ..1..1....1..1....0..1....0..1....1..0....1..0....1..0....1..0....0..1....0..1
%Y Cf. A183413.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 04 2011
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