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

1

`%I #9 Jun 16 2017 05:26:18
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`%S 0,48,480,4032,31104,228096,1617408,11197440,76142592,510603264,
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`%T 3386105856,22251552768,145118822400,940369969152,6060162023424,
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`%U 38868625391616,248257671856128,1579821548175360,10020582391283712
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`%N Number of defective 3-colorings of an n X 3 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
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`%C Column 3 of A229510
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`%H R. H. Hardin, <a href="/A229505/b229505.txt">Table of n, a(n) for n = 1..210</a>
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`%F Empirical: a(n) = 12*a(n-1) - 36*a(n-2) for n>3.
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`%F Conjectures from _Colin Barker_, Jun 16 2017: (Start)
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`%F G.f.: 48*x^2*(1 - 2*x) / (1 - 6*x)^2.
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`%F a(n) = 2^(2+n)*3^(n-2)*(2*n - 1) for n>1.
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`%F (End)
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`%e Some solutions for n=4
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`%e ..0..0..1....0..1..2....0..1..1....0..1..0....0..1..2....0..1..0....0..1..0
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`%e ..2..2..2....2..1..2....2..2..0....0..2..0....0..1..0....2..2..2....2..1..2
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`%e ..0..1..1....0..1..0....0..1..1....1..1..0....1..1..2....1..0..0....1..0..2
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`%e ..1..2..0....1..2..2....2..2..1....0..2..1....0..0..2....1..2..0....2..0..1
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`%K nonn
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`%O 1,2
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`%A _R. H. Hardin_, Sep 25 2013
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