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%I #8 Oct 09 2018 14:38:41
%S 48,512,18432,720896,31457280,1543503872,83751862272,4879082848256,
%T 296868139499520,18506979718725632,1168684103302643712,
%U 74291379453103702016,4738507383934141071360,302747963737721161121792
%N Number of n X 5 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).
%H R. H. Hardin, <a href="/A233165/b233165.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 96*a(n-1) - 2048*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Oct 09 2018: (Start)
%F G.f.: 16*x*(3 - 256*x + 4224*x^2) / ((1 - 32*x)*(1 - 64*x)).
%F a(n) = 2^(5*n-6) * (2^n+28) for n>1.
%F (End)
%e Some solutions for n=3:
%e ..0..1..7..2..7....0..1..7..6..2....0..1..2..3..2....0..1..2..1..2
%e ..3..2..3..6..4....5..3..2..3..0....2..3..7..1..7....2..3..7..3..7
%e ..0..6..7..2..0....0..6..7..6..5....7..6..2..3..5....0..6..5..1..2
%Y Column 5 of A233168.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 05 2013
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