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A233020 Number of n X 2 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

%I A233020 #9 May 11 2022 10:28:40
%S A233020 3,15,81,435,2337,12555,67449,362355,1946673,10458075,56183721,
%T A233020 301834755,1621541217,8711375595,46799960409,251422553235,
%U A233020 1350712686993,7256408541435,38983468081161,209430157488675,1125117723605697
%N A233020 Number of n X 2 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.
%H A233020 R. H. Hardin, <a href="/A233020/b233020.txt">Table of n, a(n) for n = 1..210</a>
%F A233020 Empirical: a(n) = 5*a(n-1) + 2*a(n-2).
%F A233020 Conjectures from _Colin Barker_, Oct 06 2018: (Start)
%F A233020 G.f.: 3*x / (1 - 5*x - 2*x^2).
%F A233020 a(n) = sqrt(3/11)*(((5+sqrt(33))/2)^n - ((5-sqrt(33))/2)^n) = 3*A015535(n).
%F A233020 (End)
%e A233020 Some solutions for n=5:
%e A233020 ..0..2....0..0....0..0....0..1....0..0....0..0....0..1....0..2....0..0....0..0
%e A233020 ..2..2....1..1....2..2....1..1....1..1....0..2....0..1....2..0....1..1....0..0
%e A233020 ..3..2....1..1....2..3....0..0....0..0....2..2....0..1....2..0....1..1....1..1
%e A233020 ..3..2....1..3....3..3....2..2....1..1....2..3....0..1....0..2....3..3....3..1
%e A233020 ..2..3....3..3....3..2....0..0....3..1....2..3....0..1....0..2....2..3....3..1
%Y A233020 Column 2 of A233026.
%K A233020 nonn
%O A233020 1,1
%A A233020 _R. H. Hardin_, Dec 03 2013