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Number of n X 2 0..1 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 3 0..1 array.
1

%I #12 Sep 13 2018 09:47:27

%S 4,16,64,252,992,3900,15328,60228,236624,929580,3651712,14344836,

%T 56349296,221349132,869490976,3415475172,13416415184,52701313836,

%U 207017071552,813187592388,3194296661552,12547572276300,49288333901920

%N Number of n X 2 0..1 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 3 0..1 array.

%H R. H. Hardin, <a href="/A228980/b228980.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 6*a(n-3) + 6*a(n-4).

%F Empirical g.f.: 4*x*(1 - 2*x - x^2 + x^3) / (1 - 6*x + 7*x^2 + 6*x^3 - 6*x^4). - _Colin Barker_, Sep 13 2018

%e Some solutions for n=4:

%e ..0..1....1..0....0..1....0..1....1..0....1..0....1..1....1..1....0..1....1..0

%e ..1..0....1..1....0..1....0..0....1..1....1..0....0..1....0..0....0..0....1..1

%e ..0..0....0..1....0..0....1..1....1..1....1..0....1..0....1..1....0..0....0..0

%e ..1..0....0..1....0..1....1..1....1..0....1..0....1..1....1..0....0..1....1..0

%Y Column 2 of A228986.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 10 2013