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A186454 Number of (n+1) X 2 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

%I A186454 #8 Feb 28 2018 08:34:17
%S A186454 16,21,42,61,106,151,245,359,567,840,1301,1941,2977,4465,6810,10247,
%T A186454 15577,23487,35635,53800,81533,123193,186569,282037,426954,645623,
%U A186454 977117,1477831,2236287,3382632,5118213,7742397,11714273,17721097,26811194
%N A186454 Number of (n+1) X 2 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
%C A186454 Column 1 of A186462.
%H A186454 R. H. Hardin, <a href="/A186454/b186454.txt">Table of n, a(n) for n = 1..200</a>
%F A186454 Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>8.
%F A186454 Empirical g.f.: x*(16 - 11*x + 9*x^3 - 6*x^4 - 3*x^5 + 2*x^6 + x^7) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - _Colin Barker_, Feb 28 2018
%e A186454 Some solutions for 3 X 2:
%e A186454 ..1..0....1..0....1..0....0..1....0..0....1..0....1..0....0..0....0..0....1..0
%e A186454 ..1..0....0..0....0..1....0..1....1..0....0..0....0..1....0..0....1..0....1..0
%e A186454 ..0..1....0..1....1..0....0..1....0..1....0..0....0..0....0..0....1..1....1..0
%Y A186454 Cf. A186462.
%K A186454 nonn
%O A186454 1,1
%A A186454 _R. H. Hardin_, Feb 22 2011