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%I #8 May 03 2018 07:02:48
%S 512,112,228,415,616,880,1205,1508,2008,2793,3776,5220,7274,9829,
%T 13345,18256,24651,33451,45700,61988,84197,114766,155769,211493,
%U 287826,390881,530866,722029,980917,1332459,1811512,2461345,3343817,4544963,6175777
%N Number of (n+2) X 3 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.
%C Column 1 of A190033.
%H R. H. Hardin, <a href="/A190025/b190025.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) +a(n-6) -a(n-7) for n>11.
%F Empirical g.f.: x*(512 - 912*x + 516*x^2 - 441*x^3 + 926*x^4 - 453*x^5 - 522*x^6 + 364*x^7 + 18*x^8 + 37*x^9 + 19*x^10) / ((1 - x)*(1 - x - x^3 + x^4 - x^6)). - _Colin Barker_, May 03 2018
%e Some solutions for 4 X 3:
%e ..1..1..0....1..1..0....0..0..0....0..0..0....1..1..1....1..1..1....1..0..0
%e ..1..1..0....0..1..1....0..0..0....0..0..0....0..0..0....0..1..1....0..1..0
%e ..1..1..0....0..1..0....0..0..0....1..1..0....0..0..0....0..0..0....0..1..0
%e ..0..1..1....0..0..1....1..1..0....0..0..1....0..0..0....0..0..0....0..1..0
%Y Cf. A190033.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 04 2011
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