%I #8 Apr 17 2018 14:09:45
%S 42,51,111,162,270,362,590,846,1362,1998,3122,4622,7126,10642,16286,
%T 24442,37230,56046,85138,128414,194754,294094,445590,673362,1019630,
%U 1541514,2333390,3528654,5340178,8076974,12221906,18487374,27972502
%N Number of (n+1) X 4 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
%C Column 3 of A186462.
%H R. H. Hardin, <a href="/A186456/b186456.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>9.
%F Empirical g.f.: x*(42 - 33*x + 9*x^2 + 24*x^3 - 36*x^4 - 16*x^5 + 19*x^6 - 7*x^7 + 16*x^8) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - _Colin Barker_, Apr 17 2018
%e Some solutions for 3 X 4:
%e ..1..0..0..0....1..1..0..1....0..0..0..0....0..0..0..1....1..0..0..1
%e ..0..0..0..0....1..0..1..0....1..0..0..0....0..0..0..0....1..0..0..0
%e ..0..0..0..0....0..1..0..1....1..1..0..0....1..0..0..0....1..0..0..0
%Y Cf. A186462.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 22 2011