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Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
1

%I #8 Sep 28 2018 15:19:22

%S 7,8,15,20,31,52,95,180,351,692,1375,2740,5471,10932,21855,43700,

%T 87391,174772,349535,699060,1398111,2796212,5592415,11184820,22369631,

%U 44739252,89478495,178956980,357913951,715827892,1431655775,2863311540,5726623071

%N Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%H R. H. Hardin, <a href="/A231390/b231390.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(7 - 6*x - 8*x^2 - 4*x^3 - 8*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)). - _Colin Barker_, Sep 28 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 2 of A231396.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 08 2013