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%I #8 Apr 18 2018 06:25:47
%S 277,243,942,1203,3190,4023,9982,13985,32390,48553,105436,165842,
%T 344498,562526,1130820,1898670,3724364,6385226,12298364,21417538,
%U 40692652,71701562,134848628,239701634,447381180,800490426,1485546884,2671168754
%N Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
%C Column 3 of A186472.
%H R. H. Hardin, <a href="/A186466/b186466.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + 4*a(n-4) - 2*a(n-5) for n>12.
%F Empirical g.f.: x*(277 - 311*x + 179*x^2 + 184*x^3 - 294*x^4 - 210*x^5 + 276*x^6 - 170*x^7 + 176*x^8 + 4*x^9 - 2*x^10 + x^11) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - _Colin Barker_, Apr 18 2018
%e Some solutions for 3 X 4:
%e ..1..0..1..0....0..0..0..0....1..2..0..1....0..0..0..0....1..0..0..0
%e ..0..1..0..1....1..0..0..0....2..0..2..0....0..0..0..0....0..1..0..0
%e ..2..0..1..2....0..1..0..0....0..2..0..2....1..0..0..2....1..0..1..1
%Y Cf. A186472.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 22 2011
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