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Number of defective 3-colorings of a 3 X n 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
1

%I #7 Sep 19 2018 15:14:17

%S 0,40,264,1620,9156,49848,264300,1374048,7036116,35600376,178380156,

%T 886616784,4377006372,21483378600,104919416268,510169843584,

%U 2471194910580,11929478452824,57413851328028,275566856985648

%N Number of defective 3-colorings of a 3 X n 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.

%H R. H. Hardin, <a href="/A229588/b229588.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n>6.

%F Empirical g.f.: 4*x^2*(10 - 34*x + 35*x^2 - 47*x^3 + 37*x^4) / (1 - 5*x + 2*x^2)^2. - _Colin Barker_, Sep 19 2018

%e Some solutions for n=3:

%e ..0..1..2....0..1..2....0..1..1....0..1..0....0..1..1....0..0..1....0..1..2

%e ..0..2..1....0..1..2....2..0..1....2..0..2....0..2..0....2..0..1....2..1..2

%e ..1..0..1....0..0..2....2..0..1....2..1..0....0..1..2....1..0..2....0..0..2

%Y Row 3 of A229586.

%K nonn

%O 1,2

%A _R. H. Hardin_, Sep 26 2013