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%I #9 Apr 25 2018 12:02:03
%S 16,43,130,391,1173,3520,10558,31672,95004,284980,854840,2564222,
%T 7691771,23072626,69209824,207605302,622743418,1868012800,5603386130,
%U 16808201791,50418736274,151238603566,453663001075,1360830592810,4082016602475
%N Number of (n+1) X 2 binary arrays with no 2 X 2 subblock commuting with any of its horizontal and vertical 2 X 2 subblock neighbors.
%C Column 1 of A187729.
%H R. H. Hardin, <a href="/A187721/b187721.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 5*a(n-2) + 10*a(n-3) + 8*a(n-4) - 2*a(n-5) - 10*a(n-6) - 7*a(n-7) + 3*a(n-9) + a(n-10) for n>11.
%F Empirical g.f.: x*(16 + 43*x + 50*x^2 + 16*x^3 - 35*x^4 - 47*x^5 - 11*x^6 + 16*x^7 + 13*x^8 - 2*x^9 - 2*x^10) / (1 - 5*x^2 - 10*x^3 - 8*x^4 + 2*x^5 + 10*x^6 + 7*x^7 - 3*x^9 - x^10). - _Colin Barker_, Apr 25 2018
%e Some solutions for 3 X 2:
%e ..1..0....0..0....1..1....1..1....0..0....0..1....1..0....1..1....0..1....0..1
%e ..1..1....1..1....1..1....0..0....1..1....1..1....1..1....1..0....1..1....0..0
%e ..1..1....1..1....0..1....1..1....0..0....1..1....0..1....1..1....0..0....1..0
%Y Cf. A187729.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 13 2011
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