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A229582 Number of defective 3-colorings of an n X 4 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.

%I A229582 #8 Sep 19 2018 08:49:48
%S A229582 6,116,1620,19764,224532,2440692,25745364,265720500,2697594516,
%T A229582 27033340788,268094978388,2636009007156,25732468879380,
%U A229582 249667710249204,2409688805255892,23151313964420532,221538858133842324
%N A229582 Number of defective 3-colorings of an n X 4 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
%H A229582 R. H. Hardin, <a href="/A229582/b229582.txt">Table of n, a(n) for n = 1..210</a>
%F A229582 Empirical: a(n) = 18*a(n-1) - 81*a(n-2) for n>3.
%F A229582 Conjectures from _Colin Barker_, Sep 19 2018: (Start)
%F A229582 G.f.: 2*x*(3 + 4*x + 9*x^2) / (1 - 9*x)^2.
%F A229582 a(n) = 4 * 9^(n - 2) * (16*n - 3) for n>1.
%F A229582 (End)
%e A229582 Some solutions for n=3:
%e A229582 ..0..1..0..1....0..1..1..2....0..1..0..2....0..1..2..1....0..1..2..0
%e A229582 ..0..2..1..2....0..2..0..2....0..1..0..2....0..1..0..1....1..0..1..0
%e A229582 ..1..0..1..0....0..2..1..0....1..2..1..2....1..2..0..2....1..2..1..0
%Y A229582 Column 4 of A229586.
%K A229582 nonn
%O A229582 1,1
%A A229582 _R. H. Hardin_, Sep 26 2013