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%I #8 Oct 09 2018 15:13:13
%S 1248,32768,4325376,587202560,83751862272,12919261626368,
%T 2216615441596416,427841964600197120,91657259616244334592,
%U 21176862196618565255168,5128490000396434702073856
%N Number of n X 7 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="/A233167/b233167.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 384*a(n-1) - 32768*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Oct 09 2018: (Start)
%F G.f.: 32*x*(39 - 13952*x + 1019904*x^2) / ((1 - 128*x)*(1 - 256*x)).
%F a(n) = 2^(7*n-6) * (2^n+124) for n>1.
%F (End)
%e Some solutions for n=2:
%e ..0..1..2..1..2..1..2....0..1..2..6..7..6..0....0..1..2..6..7..1..5
%e ..2..3..0..3..0..4..0....5..3..7..4..2..3..5....5..3..7..3..2..4..7
%Y Column 7 of A233168.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 05 2013
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