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A231747 Number of n X 2 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

%I A231747 #9 Sep 30 2018 20:23:18
%S A231747 3,15,51,186,687,2485,9068,33308,121445,444183,1626731,5949198,
%T A231747 21774916,79713938,291767058,1068145321,3910543065,14316731138,
%U A231747 52417430039,191916565888,702674552025,2572785049162,9420099176524,34491356066515
%N A231747 Number of n X 2 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.
%H A231747 R. H. Hardin, <a href="/A231747/b231747.txt">Table of n, a(n) for n = 1..210</a>
%F A231747 Empirical: a(n) = 3*a(n-1) + 3*a(n-2) + 14*a(n-3) - 39*a(n-4) - 45*a(n-5) - 124*a(n-6) + 18*a(n-7) + 132*a(n-8) + 248*a(n-9) + 112*a(n-10) + 64*a(n-11).
%F A231747 Empirical g.f.: x*(3 + 6*x - 3*x^2 - 54*x^3 - 117*x^4 - 128*x^5 - 16*x^6 + 386*x^7 + 348*x^8 + 224*x^9 + 64*x^10) / (1 - 3*x - 3*x^2 - 14*x^3 + 39*x^4 + 45*x^5 + 124*x^6 - 18*x^7 - 132*x^8 - 248*x^9 - 112*x^10 - 64*x^11). - _Colin Barker_, Sep 30 2018
%e A231747 Some solutions for n=7:
%e A231747 ..1..0....2..2....0..2....0..0....1..0....2..1....0..0....0..0....2..0....0..2
%e A231747 ..0..0....1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%e A231747 ..0..0....1..1....0..0....0..0....0..0....0..0....0..1....1..2....0..0....0..0
%e A231747 ..0..0....1..1....2..1....1..1....0..0....0..0....0..0....1..1....0..2....0..1
%e A231747 ..1..2....2..1....0..0....2..1....1..1....0..0....0..0....1..2....0..0....0..2
%e A231747 ..1..1....2..1....0..0....1..1....1..1....2..0....2..1....1..1....0..0....0..0
%e A231747 ..1..1....1..1....1..0....1..2....1..1....0..0....1..1....1..2....0..2....0..2
%Y A231747 Column 2 of A231753.
%K A231747 nonn
%O A231747 1,1
%A A231747 _R. H. Hardin_, Nov 13 2013