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A229587 Number of defective 3-colorings of a 2 X n 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.

%I A229587 #25 Jul 23 2025 05:45:46
%S A229587 0,6,28,116,444,1620,5724,19764,67068,224532,743580,2440692,7951932,
%T A229587 25745364,82904796,265720500,848179836,2697594516,8551948572,
%U A229587 27033340788,85232507580,268094978388,841477302108,2636009007156,8242758323964
%N A229587 Number of defective 3-colorings of a 2 X n 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
%C A229587 Row 2 of A229586.
%H A229587 R. H. Hardin, <a href="/A229587/b229587.txt">Table of n, a(n) for n = 1..210</a>
%H A229587 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9).
%F A229587 a(n) = 6*a(n-1) - 9*a(n-2) for n>4.
%F A229587 From _Oboifeng Dira_, Mar 04 2015: (Start)
%F A229587 a(n) = 4*(3^(n-2) + 4*(2*n-3)*3^(n-4)) for n>2.
%F A229587 G.f.: (x + x^3 + 2*x^4)/(1-3*x)^2 (except for first term).
%F A229587 (End)
%e A229587 Some solutions for n=3
%e A229587 ..0..1..0....0..1..0....0..1..2....0..1..1....0..1..0....0..1..1....0..1..2
%e A229587 ..2..1..1....2..2..1....2..1..1....0..2..0....0..1..1....0..2..1....1..0..2
%t A229587 LinearRecurrence[{6,-9},{0,6,28,116},30] (* _Harvey P. Dale_, Mar 06 2023 *)
%K A229587 nonn
%O A229587 1,2
%A A229587 _R. H. Hardin_, Sep 26 2013