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Number of (n+1) X (2+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order.
1

%I #9 Sep 29 2018 03:12:51

%S 7,8,15,20,32,56,111,230,501,1108,2494,5646,12867,29400,67363,154548,

%T 355012,816044,1876871,4318210,9937849,22874740,52659602,121237426,

%U 279141179,642732036,1479959127,3407837396,7847200520,18069880640

%N Number of (n+1) X (2+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order.

%H R. H. Hardin, <a href="/A231458/b231458.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) for n>7.

%F Empirical g.f.: x*(7 - 13*x - 16*x^2 + 16*x^3 + 6*x^4 + 16*x^5 + 12*x^6) / ((1 - x)*(1 - x - x^2)*(1 - x - 3*x^2)). - _Colin Barker_, Sep 29 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 2 of A231463.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 09 2013