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Number of (n+1) X (2+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 #8 Oct 19 2018 13:23:52

%S 112,232,568,1624,5272,18712,70168,271384,1067032,4231192,16850968,

%T 67256344,268730392,1074331672,4296146968,17182228504,68724195352,

%U 274887344152,1099530502168,4398084259864,17592261541912,70368895172632

%N Number of (n+1) X (2+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="/A235887/b235887.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 19 2018: (Start)

%F G.f.: 8*x*(14 - 69*x + 64*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).

%F a(n) = 4*(6 + 9*2^n + 4^n).

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A235893.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 16 2014