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Number of (n+1) X (5+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
1

%I #7 Oct 20 2018 03:58:33

%S 4480,5272,6952,10696,19720,43912,116872,361096,1242760,4578952,

%T 17542792,68636296,271486600,1079840392,4307160712,17204252296,

%U 68768239240,274975428232,1099706666632,4398436585096,17592966188680,70370304462472

%N Number of (n+1) X (5+1) 0..3 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="/A235890/b235890.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3).

%F Conjectures from _Colin Barker_, Oct 20 2018: (Start)

%F G.f.: 8*x*(560 - 3261*x + 4096*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).

%F a(n) = 4*(930 + 93*2^n + 4^n).

%F (End)

%e Some solutions for n=4:

%e ..3..2..0..1..3..0....1..0..3..3..1..2....2..2..2..1..1..1....3..0..3..0..0..3

%e ..3..2..0..1..3..0....1..0..3..3..1..2....2..2..2..1..1..1....3..0..3..0..0..3

%e ..3..2..0..1..3..0....1..0..3..3..1..2....2..2..2..1..1..1....0..3..0..3..3..0

%e ..3..2..0..1..3..0....1..0..3..3..1..2....1..1..1..2..2..2....3..0..3..0..0..3

%e ..3..2..0..1..3..0....1..0..3..3..1..2....2..2..2..1..1..1....3..0..3..0..0..3

%Y Column 5 of A235893.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 16 2014