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A231258 Number of (n+1) X (3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%I A231258 #12 Feb 16 2018 09:40:44
%S A231258 4,32,304,2982,29366,289230,2848550,28054534,276301638,2721223974,
%T A231258 26800640678,263952669990,2599602461350,25602820961958,
%U A231258 252155647340198,2483416596612262,24458536057349286,240885877498412198
%N A231258 Number of (n+1) X (3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.
%C A231258 Column 3 of A231263.
%H A231258 R. H. Hardin, <a href="/A231258/b231258.txt">Table of n, a(n) for n = 1..210</a>
%F A231258 Empirical: a(n) = 17*a(n-1) -96*a(n-2) +308*a(n-3) -628*a(n-4) +800*a(n-5) -656*a(n-6) +256*a(n-7).
%F A231258 Empirical g.f.: 2*x*(2 - 18*x + 72*x^2 - 173*x^3 + 256*x^4 - 228*x^5 + 128*x^6) / ((1 - x)*(1 - 16*x + 80*x^2 - 228*x^3 + 400*x^4 - 400*x^5 + 256*x^6)). - _Colin Barker_, Feb 16 2018
%e A231258 Some solutions for n=3:
%e A231258 ..0..0..0..0....0..0..1..1....0..0..1..1....0..0..0..0....0..0..0..0
%e A231258 ..0..0..0..0....0..1..1..2....0..1..0..0....1..1..1..1....0..0..1..1
%e A231258 ..1..1..0..0....0..0..2..2....1..0..0..2....0..0..1..1....1..1..1..2
%e A231258 ..1..0..0..0....0..0..0..0....0..0..2..2....0..1..1..1....2..2..2..2
%K A231258 nonn
%O A231258 1,1
%A A231258 _R. H. Hardin_, Nov 06 2013