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A186464 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

%I A186464 #10 Feb 28 2018 09:02:19
%S A186464 81,83,277,367,966,1321,3078,4553,10028,15650,32786,53166,107524,
%T A186464 179614,353932,604474,1168188,2028530,3863852,6793514,12800564,
%U A186464 22716978,42458812,75878698,140963524,253237282,468324588,844629530,1556731220
%N A186464 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
%C A186464 Column 1 of A186472.
%H A186464 R. H. Hardin, <a href="/A186464/b186464.txt">Table of n, a(n) for n = 1..200</a>
%F A186464 Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + 4*a(n-4) - 2*a(n-5) for n>10.
%F A186464 Empirical g.f.: x*(81 - 79*x + 30*x^2 + 54*x^3 - 37*x^4 - 40*x^5 - 4*x^6 + 26*x^7 - 2*x^8 + x^9) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - _Colin Barker_, Feb 28 2018
%e A186464 Some solutions for 3 X 2:
%e A186464 ..1..1....1..0....1..0....0..1....1..2....0..0....2..2....1..2....0..0....2..0
%e A186464 ..0..0....1..0....0..0....2..0....0..0....1..0....2..0....1..0....1..0....0..2
%e A186464 ..0..0....0..1....0..2....0..2....0..0....2..1....0..2....0..1....1..1....1..1
%Y A186464 Cf. A186472.
%K A186464 nonn
%O A186464 1,1
%A A186464 _R. H. Hardin_, Feb 22 2011