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%I #8 Apr 18 2018 10:35:14
%S 205,362,701,2049,3442,8223,14492,35081,64280,150785,281928,646756,
%T 1233097,2780008,5384887,11965960,23479960,51563275,102260008,
%U 222407905,444938056,960071644,1934442193,4147066744,8404992631,17923081288
%N Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
%C Column 2 of A186482.
%H R. H. Hardin, <a href="/A186475/b186475.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-4) - 3*a(n-5) for n>13.
%F Empirical g.f.: x*(205 - 48*x - 433*x^2 + 1153*x^3 - 1116*x^4 - 110*x^5 + 336*x^6 + 112*x^7- 33*x^8 + 3*x^9 + x^10 + 2*x^12) / ((1 - x)*(1 - x - 3*x^2 + 3*x^3 - 3*x^4)). - _Colin Barker_, Apr 18 2018
%e Some solutions for 5 X 3:
%e ..2..0..2....2..1..0....0..0..3....1..2..0....3..1..0....0..2..1....0..3..0
%e ..0..2..0....2..0..1....0..0..0....1..0..2....0..0..1....0..0..2....2..0..3
%e ..1..0..2....0..2..0....0..0..0....0..1..0....0..0..0....0..0..0....0..2..0
%e ..0..1..0....3..0..2....2..0..0....0..0..1....3..0..0....3..0..0....0..0..2
%e ..0..0..1....0..3..0....0..2..2....0..0..1....2..3..0....0..3..1....0..0..0
%Y Cf. A186482.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 22 2011
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