A229749 - OEIS

%I #7 Sep 21 2018 06:00:14

%S 0,3,60,422,1840,6456,20032,57440,155904,406400,1027072,2532864,

%T 6123520,14563328,34160640,79192064,181731328,413368320,932970496,

%U 2091253760,4658823168,10321657856,22754099200,49935286272,109135790080

%N Number of defective 4-colorings of an n X 2 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..3 order.

%H R. H. Hardin, <a href="/A229749/b229749.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n>5.

%F Conjectures from _Colin Barker_, Sep 21 2018: (Start)

%F G.f.: x^2*(3 + 42*x + 98*x^2 + 4*x^3) / (1 - 2*x)^3.

%F a(n) = 2^(n-3) * (195 - 192*n + 49*n^2) for n>2.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A229755.

%K nonn

%O 1,2

%A _R. H. Hardin_, Sep 28 2013