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%I #7 Oct 19 2018 09:21:03
%S 2571,3345,4911,8097,14631,28185,56751,118257,254391,566025,1307391,
%T 3144417,7881351,20543865,55434831,153914577,436967511,1261353705,
%U 3684967071,10856716737,32173784871,95728627545,285600432111
%N Number of (n+1) X (6+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="/A235882/b235882.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*(857 - 4027*x + 4374*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
%F a(n) = 3*(602 + 63*2^(1+n) + 3^n).
%F (End)
%e Some solutions for n=5:
%e ..0..0..0..0..0..0..0....0..1..1..0..0..0..1....0..0..2..2..0..0..0
%e ..1..1..1..1..1..1..1....0..1..1..0..0..0..1....0..0..2..2..0..0..0
%e ..2..2..2..2..2..2..2....1..0..0..1..1..1..0....0..0..2..2..0..0..0
%e ..1..1..1..1..1..1..1....0..1..1..0..0..0..1....2..2..0..0..2..2..2
%e ..2..2..2..2..2..2..2....1..0..0..1..1..1..0....2..2..0..0..2..2..2
%e ..2..2..2..2..2..2..2....1..0..0..1..1..1..0....2..2..0..0..2..2..2
%Y Column 6 of A235884.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 16 2014
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