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A229679 Number of defective 3-colorings of an n X 2 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229679 #27 Jul 15 2025 18:07:07
%S A229679 0,2,36,360,2688,17280,101376,559104,2949120,15040512,74711040,
%T A229679 363331584,1736441856,8178892800,38050725888,175154135040,
%U A229679 798863917056,3614214979584,16234976378880,72464688218112,321607151124480
%N A229679 Number of defective 3-colorings of an n X 2 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
%H A229679 R. H. Hardin, <a href="/A229679/b229679.txt">Table of n, a(n) for n = 1..210</a>
%F A229679 Empirical: a(n) = 12*a(n-1) -48*a(n-2) +64*a(n-3) for n>5.
%F A229679 Empirical g.f.: 2*x^2 - 12*x^3*(3-6*x+8*x^2) / (4*x-1)^3. - _R. J. Mathar_, Sep 29 2013
%F A229679 Empirical: a(n) = 3*2^(2*n-5)*(3 - 5*n + 2*n^2) for n>2. - _Colin Barker_, Jun 13 2017
%F A229679 From _Enrique Navarrete_, Jul 08 2025: (Start)
%F A229679 The above empirical formulas are correct.
%F A229679 a(n) = 3*binomial(2*(n-1),2)*2^(2*n-5) for n >= 3.
%F A229679 a(n) = 3*A385601(2*(n-1)) for n >= 3. (End)
%e A229679 Some solutions for n=3:
%e A229679 ..0..1....0..1....0..1....0..0....0..1....0..0....0..1....0..1....0..1....0..1
%e A229679 ..1..1....1..2....1..0....1..0....1..1....0..1....2..0....1..2....2..2....1..1
%e A229679 ..1..2....2..2....2..2....1..1....0..1....2..0....2..2....0..1....2..2....2..1
%Y A229679 Column 2 of A229685.
%Y A229679 Cf. A385601.
%K A229679 nonn
%O A229679 1,2
%A A229679 _R. H. Hardin_, Sep 27 2013