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A233068 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

%I A233068 #8 Oct 07 2018 08:36:04
%S A233068 5,50,582,6854,80811,952869,11235652,132484030,1562171807,18420188169,
%T A233068 217199754056,2561088558394,30198812298187,356086188910685,
%U A233068 4198753668883532,49509171995392534,583782308982449751
%N A233068 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.
%H A233068 R. H. Hardin, <a href="/A233068/b233068.txt">Table of n, a(n) for n = 1..210</a>
%F A233068 Empirical: a(n) = 14*a(n-1) - 28*a(n-2) + 24*a(n-3) - 11*a(n-4) + 2*a(n-5) for n>6.
%F A233068 Empirical g.f.: x*(5 - 20*x + 22*x^2 - 14*x^3 + 6*x^4 - x^5) / ((1 - x)*(1 - 13*x + 15*x^2 - 9*x^3 + 2*x^4)). - _Colin Barker_, Oct 07 2018
%e A233068 Some solutions for n=5:
%e A233068 ..0..0..1....0..1..1....0..1..0....0..0..1....0..1..3....0..1..0....0..1..1
%e A233068 ..0..0..1....1..1..3....1..1..0....1..0..0....1..3..1....1..1..1....1..0..1
%e A233068 ..0..0..0....3..3..1....1..0..0....1..0..2....3..3..3....3..3..1....0..1..1
%e A233068 ..2..2..2....1..1..1....1..0..1....0..2..2....3..2..2....3..3..1....1..3..3
%e A233068 ..3..2..3....3..1..0....1..0..0....0..2..3....2..3..2....3..3..3....3..3..2
%Y A233068 Column 3 of A233073.
%K A233068 nonn
%O A233068 1,1
%A A233068 _R. H. Hardin_, Dec 03 2013