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%I #9 Oct 20 2018 10:24:25
%S 88,508,2960,17464,104112,626480,3800832,23225504,142804544,882709824,
%T 5480742912,34158067072,213553551104,1338584619776,8408369438720,
%U 52910011296256,333414947431424,2103480056239104,13283213826064384
%N Number of (n+1) X (1+1) 0..3 arrays with the minimum plus the maximum equal to the lower median plus the upper median in every 2 X 2 subblock.
%H R. H. Hardin, <a href="/A236003/b236003.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 16*a(n-1) - 86*a(n-2) + 156*a(n-3) + 48*a(n-4) - 256*a(n-5) - 64*a(n-6).
%F Empirical g.f.: 4*x*(22 - 225*x + 600*x^2 + 16*x^3 - 1056*x^4 - 256*x^5) / ((1 - 8*x + 14*x^2 + 4*x^3)*(1 - 8*x + 8*x^2 + 16*x^3)). - _Colin Barker_, Oct 20 2018
%e Some solutions for n=5:
%e ..0..2....3..2....3..1....3..2....2..3....2..1....1..2....2..1....1..3....0..3
%e ..3..1....2..1....2..2....2..1....2..1....2..3....3..2....1..2....2..2....2..1
%e ..2..2....0..1....0..0....3..0....2..1....1..2....2..3....2..3....1..1....3..2
%e ..1..3....1..2....3..3....2..1....2..1....1..0....1..0....1..2....2..2....2..3
%e ..2..0....0..1....2..2....1..2....2..1....2..3....1..2....1..2....1..3....1..2
%e ..1..1....1..0....1..3....1..2....2..1....1..0....3..2....0..1....2..2....2..1
%Y Column 1 of A236009.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 18 2014