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%I #8 Sep 07 2018 07:59:33
%S 4,13,33,81,202,492,1143,2524,5315,10718,20776,38839,70225,123134,
%T 209884,348550,565100,896136,1392363,2122925,3180764,4689176,6809757,
%U 9751952,13784441,19248618,26574442,36298963,49087851,65760282,87317562
%N Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of zero, with rows and columns of the latter in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A227122/b227122.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/362880)*n^9 + (31/60480)*n^7 + (13/17280)*n^5 + (5/12)*n^4 - (167659/90720)*n^3 + (43/12)*n^2 + (12407/1260)*n - 14 for n>2.
%F Conjectures from _Colin Barker_, Sep 07 2018: (Start)
%F G.f.: x*(4 - 27*x + 83*x^2 - 144*x^3 + 157*x^4 - 121*x^5 + 87*x^6 - 62*x^7 + 28*x^8 - x^9 - 4*x^10 + x^11) / (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>12.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....1..1..0....0..0..0
%e ..0..1..1....0..0..1....0..0..0....0..0..0....0..0..1....1..0..0....0..0..0
%e ..0..1..0....0..0..0....0..1..1....0..1..1....0..1..1....0..0..0....0..0..1
%e ..0..0..0....0..1..0....0..0..0....0..0..1....0..1..0....0..0..0....0..0..1
%Y Column 3 of A227125
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 01 2013
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