A198710 - OEIS

%I #8 Mar 02 2018 08:03:14

%S 2,25,401,6548,107042,1749965,28609241,467717288,7646461682,

%T 125007943505,2043688517681,33411178843628,546221629207922,

%U 8929887496964645,145989990956749721,2386712874803449568,39019101990629849762

%N Number of n X 3 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

%C Column 3 of A198715.

%H R. H. Hardin, <a href="/A198710/b198710.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 19*a(n-1) - 45*a(n-2) + 27*a(n-3).

%F Empirical g.f.: x*(2 - 13*x + 16*x^2) / ((1 - x)*(1 - 18*x + 27*x^2)). - _Colin Barker_, Mar 02 2018

%e Some solutions with all values from 0 to 3 for n=4:

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

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

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

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

%Y Cf. A198715.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 29 2011