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A233107 Number of n X 2 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 A233107 #8 Mar 19 2018 09:30:52
%S A233107 2,19,313,6046,123352,2565169,53692063,1126297996,23643610702,
%T A233107 496455294319,10425137467813,218924920833946,4597402575582052,
%U A233107 96545308753707469,2027450466493247563,42576452675015933896
%N A233107 Number of n X 2 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.
%C A233107 Column 2 of A233113.
%H A233107 R. H. Hardin, <a href="/A233107/b233107.txt">Table of n, a(n) for n = 1..210</a>
%F A233107 Empirical: a(n) = 29*a(n-1) - 175*a(n-2) + 147*a(n-3).
%F A233107 Conjectures from _Colin Barker_, Mar 19 2018: (Start)
%F A233107 G.f.: x*(2 - 7*x)*(1 - 16*x) / ((1 - x)*(1 - 7*x)*(1 - 21*x)).
%F A233107 a(n) = (105 + 18*7^n + 5*21^n) / 168.
%F A233107 (End)
%e A233107 Some solutions for n=5:
%e A233107 ..0..0....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e A233107 ..1..1....0..2....1..0....1..0....2..5....1..2....2..2....0..2....2..1....0..0
%e A233107 ..2..5....4..5....5..1....0..4....0..2....5..5....1..0....1..2....1..3....0..1
%e A233107 ..4..2....4..4....2..1....2..2....2..4....5..4....5..3....1..5....5..5....4..2
%e A233107 ..5..4....5..5....1..2....1..5....4..5....2..5....2..5....1..1....4..5....0..1
%Y A233107 Cf. A233113.
%K A233107 nonn
%O A233107 1,1
%A A233107 _R. H. Hardin_, Dec 04 2013