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Number of defective 4-colorings of an n X 4 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..3 order.
1

%I #7 Sep 19 2018 06:13:45

%S 6,80,171,312,568,1064,2064,4120,8384,17256,35728,74168,154080,320008,

%T 664112,1376856,2851456,5898920,12190416,25166584,51905312,106955592,

%U 220201840,452985752,931136448,1912603624,3925869584,8053064760

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

%H R. H. Hardin, <a href="/A229574/b229574.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n>7.

%F Empirical g.f.: x*(6 + 44*x - 231*x^2 + 254*x^3 - 17*x^4 - 20*x^5 + 4*x^6) / ((1 - x)^2*(1 - 2*x)^2). - _Colin Barker_, Sep 19 2018

%e Some solutions for n=3:

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

%e ..3..2..3..1....3..2..3..3....2..3..2..3....3..2..3..1....2..3..1..3

%e ..1..0..3..0....0..1..0..1....1..0..2..0....3..1..0..2....1..0..2..0

%Y Column 4 of A229578.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 26 2013