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%I #9 Sep 07 2018 08:39:09
%S 3,7,13,23,40,68,112,178,273,405,583,817,1118,1498,1970,2548,3247,
%T 4083,5073,6235,7588,9152,10948,12998,15325,17953,20907,24213,27898,
%U 31990,36518,41512,47003,53023,59605,66783,74592,83068,92248,102170,112873
%N Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of zero, with rows and columns of the latter in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A227121/b227121.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/24)*n^4 - (1/12)*n^3 + (11/24)*n^2 + (31/12)*n.
%F Conjectures from _Colin Barker_, Sep 07 2018: (Start)
%F G.f.: x*(3 - 8*x + 8*x^2 - 2*x^3) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=4:
%e ..1..0....0..0....1..0....1..1....1..1....1..0....0..0....1..1....0..0....1..1
%e ..1..0....0..0....1..0....1..0....1..1....0..0....0..0....1..1....0..1....0..0
%e ..0..0....0..0....1..0....1..0....1..1....0..0....0..1....1..0....0..1....0..0
%e ..0..0....0..0....1..0....1..0....1..1....0..0....0..1....1..0....0..0....0..1
%Y Column 2 of A227125.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 01 2013
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