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%I #7 Oct 19 2018 08:15:37
%S 129,231,453,951,2109,4911,11973,30471,80589,220191,617493,1766391,
%T 5127069,15037071,44423013,131892711,392925549,1173271551,3508804533,
%U 10504393431,31469140029,94319339631,282781858053,847993252551
%N Number of (n+1) X (3+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="/A235879/b235879.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*(43 - 181*x + 162*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
%F a(n) = 3*(12 + 7*2^(1+n) + 3^n).
%F (End)
%e Some solutions for n=5:
%e ..2..0..0..2....0..0..0..0....2..2..2..2....0..1..0..0....1..1..1..1
%e ..2..0..0..2....0..0..0..0....1..1..1..1....0..1..0..0....1..1..1..1
%e ..2..0..0..2....0..0..0..0....1..1..1..1....1..0..1..1....0..0..0..0
%e ..2..0..0..2....2..2..2..2....0..0..0..0....0..1..0..0....0..0..0..0
%e ..0..2..2..0....1..1..1..1....2..2..2..2....0..1..0..0....2..2..2..2
%e ..2..0..0..2....0..0..0..0....1..1..1..1....0..1..0..0....0..0..0..0
%Y Column 3 of A235884.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 16 2014
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