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%I #7 Sep 09 2018 09:23:40
%S 3,11,39,127,377,1014,2518,5844,12790,26582,52769,100547,184661,
%T 328068,565582,948764,1552366,2482688,3888261,5973327,9014649,
%U 13382250,19564750,28200044,40112142,56355074,78264849,107520547,146215717,196941352
%N Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having determinant equal to one, with rows and columns of the latter in nondecreasing lexicographic order.
%H R. H. Hardin, <a href="/A227638/b227638.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/90720)*n^9 - (1/6720)*n^8 + (73/15120)*n^7 - (9/160)*n^6 + (2869/4320)*n^5 - (4367/960)*n^4 + (66841/2835)*n^3 - (41101/560)*n^2 + (17105/126)*n - 108 for n>3.
%F Conjectures from _Colin Barker_, Sep 09 2018: (Start)
%F G.f.: x*(3 - 19*x + 64*x^2 - 128*x^3 + 172*x^4 - 167*x^5 + 151*x^6 - 154*x^7 + 151*x^8 - 107*x^9 + 49*x^10 - 13*x^11 + 2*x^12) / (1 - x)^10.
%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>13.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..1....0..0..1
%e ..0..0..1....0..0..0....0..1..1....0..1..0....0..1..0....0..0..0....0..0..0
%e ..0..1..0....1..0..0....1..0..0....0..0..1....0..0..0....0..0..1....1..0..1
%e ..0..1..0....0..0..1....0..1..0....1..0..1....0..1..0....0..0..0....0..0..0
%Y Column 3 of A227641.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 18 2013
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