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%I #10 Apr 18 2018 06:25:55
%S 83,129,243,562,903,1754,2937,5790,9993,19236,33546,63642,112278,
%T 210972,375366,700068,1253442,2324820,4182330,7725252,13947186,
%U 25682700,46491258,85412820,154924338,284132892,516138474,945381252,1719241122
%N Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
%C Column 2 of A186472.
%H R. H. Hardin, <a href="/A186465/b186465.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>11.
%F Empirical g.f.: x*(83 - 37*x - 98*x^2 + 279*x^3 - 280*x^4 + 8*x^5 + 60*x^6 + 12*x^7 + 4*x^8 - 2*x^9 + x^10) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - _Colin Barker_, Apr 18 2018
%e Some solutions for 5 X 3:
%e ..2..1..0....1..0..0....1..1..1....1..0..0....0..2..1....0..0..0....1..0..0
%e ..0..0..1....0..1..0....0..0..0....0..1..0....0..0..2....0..0..0....0..1..0
%e ..0..0..1....1..0..1....0..0..0....1..0..1....0..0..0....0..0..0....0..0..1
%e ..0..0..1....0..1..1....2..0..0....0..1..0....1..0..0....2..0..0....0..0..0
%e ..0..0..1....1..1..2....0..2..1....1..0..1....1..1..0....0..2..1....1..0..0
%Y Cf. A186472.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 22 2011