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%I #8 Feb 24 2018 09:25:21
%S 0,2,6,20,68,230,778,2632,8904,30122,101902,344732,1166220,3945294,
%T 13346834,45152016,152748176,516743378,1748130326,5913882532,
%U 20006521300,67681576758,228965134106,774583500376,2620397211992,8864740270458
%N Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
%C Column 2 of A231063.
%H R. H. Hardin, <a href="/A231057/b231057.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) + a(n-2) + a(n-3).
%F Empirical g.f.: 2*x^2 / (1 - 3*x - x^2 - x^3). - _Colin Barker_, Feb 24 2018
%e Some solutions for n=4:
%e ..0..1....0..3....0..3....0..1....0..1....0..1....0..1....0..1....0..3....0..1
%e ..1..2....1..2....1..0....3..2....3..2....3..2....3..2....3..2....1..2....1..2
%e ..2..3....0..3....2..3....1..0....2..1....0..3....2..1....2..3....0..1....0..3
%e ..1..0....3..2....1..2....2..3....3..0....1..2....1..0....1..0....3..2....1..2
%Y Cf. A231063.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 03 2013