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A233108 Number of n X 3 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

%I A233108 #7 Oct 07 2018 14:35:07
%S A233108 6,313,24912,2154065,189286871,16683923848,1471365099497,
%T A233108 129774107522700,11446271884607256,1009582054691903383,
%U A233108 89047037607095248482,7854117302435219663735,692748031461206544348041
%N A233108 Number of n X 3 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
%H A233108 R. H. Hardin, <a href="/A233108/b233108.txt">Table of n, a(n) for n = 1..210</a>
%F A233108 Empirical: a(n) = 111*a(n-1) - 2128*a(n-2) + 10532*a(n-3) - 17559*a(n-4) + 9045*a(n-5).
%F A233108 Empirical g.f.: x*(6 - 353*x + 2937*x^2 - 8295*x^3 + 7230*x^4) / ((1 - x)*(1 - 18*x + 27*x^2)*(1 - 92*x + 335*x^2)). - _Colin Barker_, Oct 07 2018
%e A233108 Some solutions for n=3:
%e A233108 ..0..1..0....0..1..1....0..0..1....0..1..5....0..1..5....0..1..0....0..1..1
%e A233108 ..2..1..0....2..1..2....2..0..2....2..2..4....1..2..1....0..2..1....2..0..0
%e A233108 ..0..1..0....1..0..0....4..0..2....0..1..0....0..0..0....2..1..3....5..1..2
%Y A233108 Column 3 of A233113.
%K A233108 nonn
%O A233108 1,1
%A A233108 _R. H. Hardin_, Dec 04 2013