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%I #10 Apr 05 2020 22:12:58
%S 4,11,34,104,285,683,1469,2906,5383,9457,15904,25780,40493,61887,
%T 92339,134870,193271,272245,377566,516256,696781,929267,1225737,
%U 1600370,2069783,2653337,3373468,4256044,5330749,6631495,8196863,10070574
%N Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having two adjacent 1's and two adjacent 0's, with rows and columns of the latter in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A227329/b227329.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/5040)*n^7 + (1/720)*n^6 + (37/720)*n^5 - (1/144)*n^4 + (283/180)*n^3 - (1259/180)*n^2 + (3019/210)*n - 2 for n>2.
%F Conjectures from _Colin Barker_, Sep 08 2018: (Start)
%F G.f.: x*(4 - 21*x + 58*x^2 - 84*x^3 + 69*x^4 - 43*x^5 + 37*x^6 - 30*x^7 + 13*x^8 - 2*x^9) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for x>10.
%F (End)
%e Some solutions for n=4:
%e ..0..0....0..0....0..0....0..1....0..1....1..0....1..0....0..0....0..0....0..0
%e ..0..1....0..0....1..1....1..0....0..0....0..0....1..0....0..0....1..1....0..1
%e ..0..0....1..1....0..1....1..0....0..0....1..1....0..1....0..0....1..1....0..0
%e ..1..1....1..0....0..1....0..0....0..0....1..1....0..1....1..0....0..0....0..0
%Y Column 2 of A227333.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 07 2013