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A233123 Number of n X 2 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs). 2

%I

%S 1,8,80,896,10496,124928,1495040,17924096,215023616,2580021248,

%T 30959206400,371506282496,4458058612736,53496636243968,

%U 641959366492160,7703511324164096,92442131595001856,1109305561960153088

%N Number of n X 2 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

%C Column 2 of A233129.

%H R. H. Hardin, <a href="/A233123/b233123.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 48*a(n-2).

%F Conjectures from _Colin Barker_, Mar 19 2018: (Start)

%F G.f.: x*(1 - 8*x) / ((1 - 4*x)*(1 - 12*x)).

%F a(n) = 2^(2*n-3) * (3^n+3) / 3.

%F (End)

%e Some solutions for n=5:

%e ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1

%e ..1..0....2..5....4..0....4..0....2..0....2..5....4..0....4..0....1..0....1..0

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

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

%e ..0..4....0..2....0..2....2..4....0..4....1..3....0..1....0..2....1..0....0..1

%Y A233129.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 04 2013

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Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)