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A231317 Number of (n+1) X (1+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%I A231317 #8 Mar 18 2018 06:59:15
%S A231317 6,24,216,1536,11616,86400,645504,4816896,35956224,268376064,
%T A231317 2003195904,14952038400,111603572736,833020329984,6217748545536,
%U A231317 46409906651136,346408259813376,2585626450329600,19299378566529024,144052522724622336
%N A231317 Number of (n+1) X (1+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
%C A231317 Column 1 of A231324.
%H A231317 R. H. Hardin, <a href="/A231317/b231317.txt">Table of n, a(n) for n = 1..210</a>
%F A231317 Empirical: a(n) = 6*a(n-1) + 12*a(n-2) - 8*a(n-3).
%F A231317 Conjectures from _Colin Barker_, Mar 18 2018: (Start)
%F A231317 G.f.: 6*x*(1 - 2*x) / ((1 + 2*x)*(1 - 8*x + 4*x^2)).
%F A231317 a(n) = ((-2)^(1+n) + (4-2*sqrt(3))^n + (2*(2+sqrt(3)))^n) / 2.
%F A231317 (End)
%e A231317 Some solutions for n=4:
%e A231317 ..0..0....0..1....0..1....0..0....0..1....0..1....0..0....0..1....0..1....0..0
%e A231317 ..1..1....2..2....0..2....1..1....2..2....2..2....1..2....0..2....2..1....1..2
%e A231317 ..2..1....1..2....0..0....0..0....0..2....0..1....0..1....1..2....2..1....0..1
%e A231317 ..2..2....1..0....1..1....1..0....0..1....2..0....0..1....2..1....1..2....0..2
%e A231317 ..1..0....1..2....2..0....1..2....0..2....1..1....0..1....0..0....1..0....1..2
%Y A231317 Cf. A231324.
%K A231317 nonn
%O A231317 1,1
%A A231317 _R. H. Hardin_, Nov 07 2013