%I #12 Apr 19 2018 03:28:04
%S 721,173,401,1411,2617,3379,4033,4795,6361,10443,17153,26995,43177,
%T 66139,98497,151699,231881,350539,543249,835843,1270105,1958875,
%U 3007777,4577331,7041321,10810763,16490033,25335715,38890105,59403259,91177217
%N Number of (n+2) X 4 0..2 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.
%C Column 2 of A186568.
%H R. H. Hardin, <a href="/A186561/b186561.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) + 2*a(n-6) - 2*a(n-7) for n>10.
%F Empirical g.f.: x*(721 - 1269*x + 776*x^2 - 660*x^3 + 2734*x^4 - 1996*x^5 - 3114*x^6 + 812*x^7 + 1236*x^8 + 712*x^9) / ((1 - x)*(1 - x - 2*x^3 + 2*x^4 - 2*x^6)). - _Colin Barker_, Apr 18 2018
%e Some solutions for 6 X 4:
%e 0 0 1 0 2 0 0 0 0 0 0 2 0 0 2 0 0 0 0 1
%e 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
%e 1 0 0 0 0 0 0 0 1 2 0 0 2 0 0 0 2 0 0 0
%e 0 1 0 0 0 0 0 1 1 1 2 0 0 0 0 0 0 2 0 0
%Y Cf. A186568.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 23 2011