A229314 - OEIS

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 #9 Sep 14 2018 12:14:29

%S 4,14,50,176,622,2196,7756,27390,96730,341606,1206400,4260462,

%T 15046040,53135856,187651986,662702554,2340367858,8265128408,

%U 29188722358,103081461140,364037435444,1285616763070,4540221143674,16034022443998

%N 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 R. H. Hardin, <a href="/A229314/b229314.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - a(n-3) + 2*a(n-4).

%F 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 Some solutions for n=3:

%e ..1....3....2....0....0....1....2....2....0....1....3....3....2....2....2....1

%e ..3....0....0....2....1....1....2....3....3....3....1....2....1....1....3....3

%e ..1....2....3....2....0....1....2....2....2....0....1....0....1....0....1....2

%Y Column 1 of A229320.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 19 2013