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A229314 Number of n X 1 0..3 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1) X 2 0..3 array without adjacent equal elements in the latter.

%I A229314 #9 Sep 14 2018 12:14:29
%S A229314 4,14,50,176,622,2196,7756,27390,96730,341606,1206400,4260462,
%T A229314 15046040,53135856,187651986,662702554,2340367858,8265128408,
%U A229314 29188722358,103081461140,364037435444,1285616763070,4540221143674,16034022443998
%N A229314 Number of n X 1 0..3 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1) X 2 0..3 array without adjacent equal elements in the latter.
%H A229314 R. H. Hardin, <a href="/A229314/b229314.txt">Table of n, a(n) for n = 1..210</a>
%F A229314 Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - a(n-3) + 2*a(n-4).
%F A229314 Empirical g.f.: 2*x*(1 + x)*(2 - x + x^2) / (1 - 3*x - 2*x^2 + x^3 - 2*x^4). - _Colin Barker_, Sep 14 2018
%e A229314 Some solutions for n=3:
%e A229314 ..1....3....2....0....0....1....2....2....0....1....3....3....2....2....2....1
%e A229314 ..3....0....0....2....1....1....2....3....3....3....1....2....1....1....3....3
%e A229314 ..1....2....3....2....0....1....2....2....2....0....1....0....1....0....1....2
%Y A229314 Column 1 of A229320.
%K A229314 nonn
%O A229314 1,1
%A A229314 _R. H. Hardin_, Sep 19 2013