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A233197 Number of n X 3 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, 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).

%I A233197 #8 Oct 10 2018 08:29:46
%S A233197 3,36,1440,62720,2779136,123551744,5496242176,244533166080,
%T A233197 10879798083584,484067845865472,21537343823413248,958248525617954816,
%U A233197 42634797465737363456,1896925413514655301632,84398806858761213313024
%N A233197 Number of n X 3 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, 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 A233197 R. H. Hardin, <a href="/A233197/b233197.txt">Table of n, a(n) for n = 1..210</a>
%F A233197 Empirical: a(n) = 64*a(n-1) - 960*a(n-2) + 4096*a(n-3) for n>4.
%F A233197 Empirical g.f.: x*(3 - 156*x + 2016*x^2 - 7168*x^3) / ((1 - 8*x)*(1 - 56*x + 512*x^2)). - _Colin Barker_, Oct 10 2018
%e A233197 Some solutions for n=4:
%e A233197 ..0..1..7....0..1..2....0..1..0....0..1..2....0..1..2....0..1..2....0..1..2
%e A233197 ..2..3..1....3..0..1....2..3..1....3..7..6....5..7..6....3..7..1....5..3..7
%e A233197 ..7..2..0....2..3..7....6..0..5....1..5..4....6..5..3....2..4..2....0..5..1
%e A233197 ..3..6..2....7..5..1....3..6..0....4..6..5....0..1..0....7..1..7....3..7..2
%Y A233197 Column 3 of A233202.
%K A233197 nonn
%O A233197 1,1
%A A233197 _R. H. Hardin_, Dec 05 2013