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%I #7 Sep 09 2018 09:23:32
%S 2,5,11,23,44,78,130,206,313,459,653,905,1226,1628,2124,2728,3455,
%T 4321,5343,6539,7928,9530,11366,13458,15829,18503,21505,24861,28598,
%U 32744,37328,42380,47931,54013,60659,67903,75780,84326,93578,103574,114353
%N Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having determinant equal to one, with rows and columns of the latter in nondecreasing lexicographic order.
%H R. H. Hardin, <a href="/A227637/b227637.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/24)*n^4 - (1/12)*n^3 + (35/24)*n^2 - (29/12)*n + 4 for n>1.
%F Conjectures from _Colin Barker_, Sep 09 2018: (Start)
%F G.f.: x*(2 - 5*x + 6*x^2 - 2*x^3 - x^4 + x^5) / (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 ..0..0....0..0....0..0....0..1....0..0....0..0....0..0....0..1....0..0....0..0
%e ..0..1....0..0....0..0....0..0....0..1....0..1....0..1....1..0....0..0....0..1
%e ..0..0....0..0....1..0....1..0....0..0....0..1....1..0....0..0....0..0....0..1
%e ..0..1....1..0....0..0....0..0....0..0....0..0....0..0....0..1....0..1....1..0
%Y Column 2 of A227641.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 18 2013
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