%I #9 Jun 15 2018 12:00:04

%S 1,17,230,3284,47060,674564,9669452,138605744,1986829652,28480003748,

%T 408243662612,5851926480128,83883833763260,1202424123191348,

%U 17236024000927580,247068000076467824,3541570646368426820

%N Number of n X 3 0..4 arrays with no element equal to another within two positions in the same row or column, and new values 0..4 introduced in row major order.

%C Column 3 of A206359.

%H R. H. Hardin, <a href="/A206354/b206354.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 20*a(n-2) - 58*a(n-3) + 33*a(n-4) + 30*a(n-5) for n>6.

%F Empirical g.f.: x*(1 + x - 22*x^2 + 2*x^3 + 69*x^4 + 33*x^5) / ((1 - x)*(1 - 15*x + 5*x^2 + 63*x^3 + 30*x^4)). - _Colin Barker_, Jun 15 2018

%e Some solutions for n=4:

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

%e ..2..0..1....1..0..3....1..0..3....3..2..4....1..3..4....1..2..3....2..3..1

%e ..1..2..3....2..3..4....2..4..0....4..3..1....2..4..3....2..0..4....1..4..0

%e ..3..4..2....3..1..2....4..1..2....2..4..3....3..0..1....3..1..2....3..0..2

%Y Cf. A206359.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 06 2012