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Number of n X 1 0..2 arrays with no average of any element and its horizontal and vertical neighbors equal to one.
2

%I #8 Mar 02 2018 14:13:54

%S 2,6,10,22,52,114,260,600,1374,3162,7290,16796,38722,89296,205916,

%T 474882,1095218,2525902,5825564,13435770,30987588,71468368,164831598,

%U 380160714,876787090,2022186212,4663888698,10756605360,24808602932,57217567106

%N Number of n X 1 0..2 arrays with no average of any element and its horizontal and vertical neighbors equal to one.

%C Column 1 of A200579.

%H R. H. Hardin, <a href="/A200572/b200572.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-2) + a(n-3) - 3*a(n-4) - 2*a(n-5).

%F Empirical g.f.: 2*x*(1 + x)^2*(1 - x - x^2) / (1 - 2*x - x^2 - x^3 + 3*x^4 + 2*x^5). - _Colin Barker_, Mar 02 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A200579.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 19 2011