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%I #8 Sep 07 2018 18:37:23
%S 4,16,49,132,341,836,1934,4232,8804,17501,33392,61393,109141,188181,
%T 315546,515823,823812,1287900,1974288,2972226,4400429,6414866,9218134,
%U 13070650,18303916,25336135,34690480,47016343,63113917,83962491
%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 three or less, with rows and columns of the latter in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A227266/b227266.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/362880)*n^9 + (1/40320)*n^8 + (5/12096)*n^7 + (19/2880)*n^6 - (611/17280)*n^5 + (3407/5760)*n^4 - (5281/9072)*n^3 - (66509/10080)*n^2 + (22991/504)*n - 59 for n>3.
%F Conjectures from _Colin Barker_, Sep 07 2018: (Start)
%F G.f.: x*(4 - 24*x + 69*x^2 - 118*x^3 + 146*x^4 - 162*x^5 + 177*x^6 - 156*x^7 + 90*x^8 - 31*x^9 + 9*x^10 - 4*x^11 + 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 ..1..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1
%e ..1..1..0....1..1..0....1..1..1....0..0..1....1..0..0....1..0..0....1..1..0
%e ..1..0..0....1..0..0....1..0..1....0..0..1....1..0..0....1..0..0....1..1..0
%e ..1..0..0....1..0..0....1..0..0....0..0..0....1..0..0....1..0..1....1..0..0
%Y Column 3 of A227269.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 04 2013
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