%I #9 Apr 19 2018 11:07:59
%S 2428,421,1201,6829,14221,18517,21661,25381,34645,64384,118027,201190,
%T 355210,592102,945346,1600378,2664955,4328077,7358623,12328480,
%U 20153704,34046296,56950552,93410275,157163740,262861768,432701869,726100972
%N Number of (n+2) X 4 0..3 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.
%C Column 2 of A186881.
%H R. H. Hardin, <a href="/A186874/b186874.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-2) + 3*a(n-3) - 6*a(n-4) + 3*a(n-5) + 3*a(n-6) - 3*a(n-7) for n>10.
%F Empirical g.f.: x*(2428 - 4435*x + 2787*x^2 - 2436*x^3 + 15069*x^4 - 11457*x^5 - 22980*x^6 + 1305*x^7 + 12492*x^8 + 7047*x^9) / ((1 - x)*(1 - x - 3*x^3 + 3*x^4 - 3*x^6)). - _Colin Barker_, Apr 19 2018
%e Some solutions for 6 X 4:
%e ..0..0..2..0....1..0..0..0....0..0..3..0....1..0..0..0....1..1..1..1
%e ..0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..3....0..0..0..0
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e ..3..0..0..0....3..0..0..0....2..0..0..0....0..0..0..0....3..0..0..0
%e ..2..3..0..0....0..2..0..0....2..2..0..0....0..0..0..3....3..1..0..0
%Y Cf. A186881.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 28 2011