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A209094 Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

%I A209094 #9 Mar 07 2018 16:50:19
%S A209094 2,11,82,612,4568,34096,254496,1899584,14178688,105831168,789934592,
%T A209094 5896152064,44009478144,328491216896,2451891822592,18301169713152,
%U A209094 136601790414848,1019609644466176,7610469994070016,56805321374695424
%N A209094 Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
%C A209094 Column 2 of A209100.
%H A209094 R. H. Hardin, <a href="/A209094/b209094.txt">Table of n, a(n) for n = 1..210</a>
%F A209094 Empirical: a(n) = 8*a(n-1) - 4*a(n-2) for n>3.
%F A209094 Conjectures from _Colin Barker_, Mar 07 2018: (Start)
%F A209094 G.f.: x*(2 - x)*(1 - 2*x) / (1 - 8*x + 4*x^2).
%F A209094 a(n) = ((4-2*sqrt(3))^n*(-1+sqrt(3)) + (1+sqrt(3))*(2*(2+sqrt(3)))^n) / (8*sqrt(3)) for n>1.
%F A209094 (End)
%e A209094 Some solutions for n=4:
%e A209094 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..1....0..1
%e A209094 ..1..2....1..0....1..1....1..1....1..1....1..0....1..1....1..2....2..1....2..1
%e A209094 ..2..0....0..1....0..0....2..0....2..2....0..1....2..0....0..2....2..2....2..2
%e A209094 ..0..2....0..1....2..0....0..1....1..1....1..2....1..0....2..0....1..2....0..0
%Y A209094 Cf. A209100.
%K A209094 nonn
%O A209094 1,1
%A A209094 _R. H. Hardin_, Mar 05 2012