%I #12 Feb 15 2018 12:18:08
%S 8274,1482,3013,5037,7661,8509,8873,9265,9825,10805,13085,16429,22789,
%T 30417,41390,53819,69824,88077,111955,140633,179247,227737,292825,
%U 375142,483400,619787,796650,1019420,1306745,1670689,2140197,2737929,3508474
%N Number of (n+3) X 8 binary arrays with every 4 X 4 subblock commuting with each horizontal and vertical neighbor 4 X 4 subblock.
%C Column 5 of A188105.
%H R. H. Hardin, <a href="/A188101/b188101.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) + a(n-8) - a(n-9) for n>15.
%F Empirical g.f.: x*(8274 - 15066*x + 8323*x^2 + 493*x^3 - 7674*x^4 + 13290*x^5 - 8807*x^6 - 465*x^7 - 8706*x^8 + 8988*x^9 + 253*x^10 - 988*x^11 + 224*x^12 + 1681*x^14) / ((1 - x)*(1 - x - x^4 + x^5 - x^8)). - _Colin Barker_, Feb 15 2018
%e Some solutions for 5 X 8:
%e ..0..0..0..0..0..1..0..0....1..1..0..0..1..1..0..0....0..0..0..0..0..0..1..0
%e ..0..0..0..0..0..0..0..0....0..1..1..0..0..1..1..0....0..0..0..0..0..0..0..1
%e ..0..0..0..0..0..0..0..0....0..0..1..1..0..0..1..1....1..0..0..0..0..0..0..0
%e ..1..0..0..0..0..0..0..0....1..0..0..1..1..0..0..1....1..0..0..0..0..0..0..0
%e ..0..0..0..0..0..0..0..0....1..1..0..0..1..1..0..0....0..1..0..0..0..0..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 20 2011
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