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A227382 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 one, with rows and columns of the latter in lexicographically nondecreasing order.

%I A227382 #9 Sep 08 2018 11:06:18
%S A227382 4,15,54,185,587,1704,4532,11126,25430,54568,110768,214130,396492,
%T A227382 706695,1217599,2035257,3310713,5254953,8157605,12410055,18533721,
%U A227382 27214306,39342934,56065160,78838936,109502710,150354934,204246360,274686610
%N A227382 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 one, with rows and columns of the latter in lexicographically nondecreasing order.
%H A227382 R. H. Hardin, <a href="/A227382/b227382.txt">Table of n, a(n) for n = 1..210</a>
%F A227382 Empirical: a(n) = (1/90720)*n^9 + (1/5760)*n^8 + (1/864)*n^7 + (1/64)*n^6 - (91/864)*n^5 + (2563/1920)*n^4 - (96743/18144)*n^3 + (5083/288)*n^2 - (10643/360)*n + 31 for n>3.
%F A227382 Conjectures from _Colin Barker_, Sep 08 2018: (Start)
%F A227382 G.f.: x*(4 - 25*x + 84*x^2 - 160*x^3 + 207*x^4 - 179*x^5 + 107*x^6 - 42*x^7 + 19*x^9 - 16*x^10 + 6*x^11 - x^12) / (1 - x)^10.
%F A227382 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 A227382 (End)
%e A227382 Some solutions for n=4:
%e A227382 ..1..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..1..0....0..0..1
%e A227382 ..0..0..0....0..1..0....0..0..0....0..0..1....1..0..0....1..0..0....0..0..0
%e A227382 ..0..1..1....0..1..0....1..0..0....0..0..0....0..0..1....0..0..1....0..0..0
%e A227382 ..0..0..0....0..0..1....0..1..1....0..1..0....0..0..1....0..1..0....1..0..0
%Y A227382 Column 3 of A227385.
%K A227382 nonn
%O A227382 1,1
%A A227382 _R. H. Hardin_, Jul 09 2013