A229666 - OEIS

A229666

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

%I #8 Sep 20 2018 09:10:32

%S 0,4,61,652,5048,33152,197248,1098752,5838848,29949952,149454848,

%T 729546752,3497525248,16517169152,77015810048,355207217152,

%U 1622826549248,7352984010752,33073395662848,147798414589952,656648959950848

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

%H R. H. Hardin, <a href="/A229666/b229666.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n>6.

%F Conjectures from _Colin Barker_, Sep 20 2018: (Start)

%F G.f.: x^2*(4 + 13*x + 112*x^2 - 104*x^3 - 32*x^4) / (1 - 4*x)^3.

%F a(n) = 2^(2*n-7) * (106 - 145*n + 50*n^2) for n>3.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Column 2 of A229672.

%K nonn

%O 1,2

%A _R. H. Hardin_, Sep 27 2013