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A233167 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 (unlabeled 8-colorings with no clashing color pairs).

%I A233167 #14 Sep 15 2024 01:58:03
%S A233167 1248,32768,4325376,587202560,83751862272,12919261626368,
%T A233167 2216615441596416,427841964600197120,91657259616244334592,
%U A233167 21176862196618565255168,5128490000396434702073856
%N A233167 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 (unlabeled 8-colorings with no clashing color pairs).
%H A233167 R. H. Hardin, <a href="/A233167/b233167.txt">Table of n, a(n) for n = 1..210</a>
%F A233167 Empirical: a(n) = 384*a(n-1) - 32768*a(n-2) for n>3.
%F A233167 Conjectures from _Colin Barker_, Oct 09 2018: (Start)
%F A233167 G.f.: 32*x*(39 - 13952*x + 1019904*x^2) / ((1 - 128*x)*(1 - 256*x)).
%F A233167 a(n) = 2^(7*n-6) * (2^n+124) for n>1. (End)
%e A233167 Some solutions for n=2:
%e A233167 ..0..1..2..1..2..1..2....0..1..2..6..7..6..0....0..1..2..6..7..1..5
%e A233167 ..2..3..0..3..0..4..0....5..3..7..4..2..3..5....5..3..7..3..2..4..7
%Y A233167 Column 7 of A233168.
%K A233167 nonn
%O A233167 1,1
%A A233167 _R. H. Hardin_, Dec 05 2013