A229472 - OEIS

%I #10 Mar 17 2018 05:45:42

%S 0,1,2,6,20,70,246,854,2920,9846,32810,108262,354300,1151462,3720094,

%T 11957430,38263760,121965718,387420498,1226831558,3874204900,

%U 12203745414,38354628422,120294061846,376572715320,1176789735350,3671583974266

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

%C Column 1 of A229479.

%H R. H. Hardin, <a href="/A229472/b229472.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 22*a(n-2) + 24*a(n-3) - 9*a(n-4) for n>6.

%F Conjectures from _Colin Barker_, Mar 16 2018: (Start)

%F G.f.: x^2*(1 - 6*x + 12*x^2 - 8*x^3 + 3*x^4) / ((1 - x)^2*(1 - 3*x)^2).

%F a(n) = (27+3^n) * (n-1) / 54 for n>2.

%F (End)

%e All solutions for n=4:

%e   0      0      0      0      0      0

%e   0      1      1      1      1      0

%e   1      0      1      2      1      1

%e   0      0      2      2      0      2

%Y Cf. A229479.

%K nonn

%O 1,3

%A _R. H. Hardin_, Sep 24 2013