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%I #7 Oct 19 2018 08:07:46
%S 51,105,231,537,1311,3345,8871,24297,68271,195585,568311,1668057,
%T 4930431,14643825,43636551,130319817,389779791,1166980065,3496221591,
%U 10479227577,31418808351,94218676305,282580531431,847590599337,2542469808111
%N Number of (n+1) X (2+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
%H R. H. Hardin, <a href="/A235878/b235878.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3).
%F Conjectures from _Colin Barker_, Oct 19 2018: (Start)
%F G.f.: 3*x*(17 - 67*x + 54*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
%F a(n) = 3*(2 + 3*2^(1+n) + 3^n).
%F (End)
%e Some solutions for n=5:
%e ..2..2..2....2..2..2....0..0..0....2..0..0....0..1..1....2..0..2....2..2..2
%e ..0..0..0....2..2..2....0..0..0....2..0..0....1..0..0....2..0..2....0..0..0
%e ..2..2..2....1..1..1....1..1..1....2..0..0....1..0..0....0..2..0....1..1..1
%e ..0..0..0....1..1..1....1..1..1....2..0..0....1..0..0....0..2..0....1..1..1
%e ..2..2..2....0..0..0....1..1..1....0..2..2....1..0..0....2..0..2....2..2..2
%e ..1..1..1....1..1..1....0..0..0....2..0..0....1..0..0....0..2..0....2..2..2
%Y Column 2 of A235884.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 16 2014