login
Number of defective 4-colorings of an n X 3 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 06:13:53

%S 2,26,76,171,362,757,1584,3323,6982,14673,30812,64615,135282,282749,

%T 589960,1228947,2556062,5308585,11010228,22806719,47186122,97517781,

%U 201326816,415236331,855638262,1761607937,3623878924,7449084183

%N Number of defective 4-colorings of an n X 3 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="/A229573/b229573.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>5.

%F Empirical g.f.: x*(2 + 14*x - 54*x^2 + 29*x^3 + 20*x^4) / ((1 - x)^2*(1 - 2*x)^2). - _Colin Barker_, Sep 19 2018

%e Some solutions for n=3:

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

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

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

%Y Column 3 of A229578.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 26 2013