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%I #7 Apr 16 2023 20:51:51
%S 24,104,472,1664,6848,27272,108128,431656,1719312,6845968,27282352,
%T 108671048,432902384,1724605424,6870205712,27368517688,109028322640,
%U 434332786176,1730241699608,6892737739416,27458456022120,109385692125040
%N Number of (n+1) X 3 binary arrays with every 2 X 2 subblock trace equal to exactly one or two horizontal and vertical neighbor 2 X 2 subblock traces.
%C Column 2 of A186939.
%H R. H. Hardin, <a href="/A186932/b186932.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n)=2*a(n-1)+4*a(n-2)+12*a(n-3)+4*a(n-4)+17*a(n-5)+136*a(n-6)-78*a(n-7)-269*a(n-8)-496*a(n-9)+226*a(n-10)+441*a(n-11)-110*a(n-12)+372*a(n-13)+448*a(n-15)-512*a(n-16).
%e Some solutions for 4 X 3
%e ..0..0..0....0..0..0....1..1..0....1..0..1....0..1..0....1..0..0....0..1..1
%e ..0..1..1....1..0..0....1..1..1....0..0..1....1..1..0....0..0..1....1..1..0
%e ..1..1..0....1..1..1....1..1..0....0..0..0....0..0..0....0..0..0....1..1..1
%e ..1..1..1....0..1..0....0..1..0....0..1..1....1..0..0....1..1..1....1..0..0
%Y Cf. A186939.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 01 2011
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