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 A233166 Number of n X 6 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). 1

%I

%S 236,4096,278528,19922944,1543503872,133143986176,12919261626368,

%T 1389782697508864,161003686678495232,19527607984278470656,

%U 2430358531711233425408,306658673481347586064384

%N Number of n X 6 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="/A233166/b233166.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 192*a(n-1) - 8192*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Oct 09 2018: (Start)

%F G.f.: 4*x*(59 - 10304*x + 356352*x^2) / ((1 - 64*x)*(1 - 128*x)).

%F a(n) = 64^(n-1) * (2^n+60) for n>1.

%F (End)

%e Some solutions for n=2:

%e ..0..1..0..6..7..2....0..1..2..6..7..3....0..1..2..6..0..1....0..1..2..3..0..6

%e ..3..5..4..2..4..6....2..4..7..4..2..1....5..3..0..4..2..4....2..3..0..1..2..4

%Y Column 6 of A233168.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 05 2013

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Last modified December 2 20:25 EST 2021. Contains 349445 sequences. (Running on oeis4.)