A184688 - OEIS

%I #11 Apr 14 2018 13:11:37

%S 9,192,4080,86688,1841856,39133824,831474432,17666296320,375354928128,

%T 7975147677696,169447570059264,3600244178460672,76494210805186560,

%U 1625268730858733568,34532004706009153536,733699803838461640704

%N 1/3 the number of n X 3 0..2 arrays with no element equal both to the element above and to the element to its left.

%C Column 3 of A184694.

%H R. H. Hardin, <a href="/A184688/b184688.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 22*a(n-1) - 16*a(n-2).

%F Conjectures from _Colin Barker_, Apr 14 2018: (Start)

%F G.f.: 3*x*(3 - 2*x) / (1 - 22*x + 16*x^2).

%F a(n) = ((105-13*sqrt(105))*(11-sqrt(105))^n + (11+sqrt(105))^n*(105+13*sqrt(105))) / 560.

%F (End)

%e Some solutions for 5 X 3 with a(1,1)=0:

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

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

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

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

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

%Y Cf. A184694.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2011