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Number of (n+1) X (1+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order.
3

%I #8 Feb 24 2018 09:25:27

%S 3,4,7,12,24,48,103,222,493,1100,2486,5638,12859,29392,67355,154540,

%T 355004,816036,1876863,4318202,9937841,22874732,52659594,121237418,

%U 279141171,642732028,1479959119,3407837388,7847200512,18069880632

%N Number of (n+1) X (1+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order.

%C Column 1 of A231343.

%H R. H. Hardin, <a href="/A231337/b231337.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + a(n-2) - 7*a(n-3) + a(n-4) + 3*a(n-5).

%F Empirical g.f.: x*(3 - 5*x - 8*x^2 + 8*x^3 + 6*x^4) / ((1 - x)*(1 - x - x^2)*(1 - x - 3*x^2)). - _Colin Barker_, Feb 24 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Cf. A231343.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2013