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A212823 Number of 0..2 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..2 order.

%I A212823 #9 Jul 21 2018 10:06:20
%S A212823 1,2,5,12,33,90,246,672,1836,5016,13704,37440,102288,279456,763488,
%T A212823 2085888,5698752,15569280,42536064,116210688,317493504,867408384,
%U A212823 2369803776,6474424320,17688456192,48325761024,132028434432,360708390912
%N A212823 Number of 0..2 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..2 order.
%C A212823 Column 2 of A212829.
%H A212823 R. H. Hardin, <a href="/A212823/b212823.txt">Table of n, a(n) for n = 1..210</a>
%F A212823 Empirical: a(n) = 2*a(n-1) + 2*a(n-2) for n>5.
%F A212823 Empirical g.f.: x*(1 - x - x^2)*(1 + x + x^2) / (1 - 2*x - 2*x^2). - _Colin Barker_, Jul 21 2018
%e A212823 Some solutions for n=8:
%e A212823 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A212823 ..1....1....1....1....1....1....0....1....1....1....0....1....1....1....1....1
%e A212823 ..2....2....1....2....2....2....0....0....2....1....1....1....0....0....2....2
%e A212823 ..1....0....0....2....2....0....1....2....0....1....2....2....2....0....0....0
%e A212823 ..0....0....2....2....0....1....2....1....0....2....2....0....1....1....2....2
%e A212823 ..0....1....0....0....1....1....2....0....0....0....0....0....0....2....2....2
%e A212823 ..1....0....0....2....0....0....1....0....1....0....0....1....2....2....0....2
%e A212823 ..1....0....1....2....0....2....2....0....1....0....2....0....1....0....1....0
%Y A212823 Cf. A212829.
%K A212823 nonn
%O A212823 1,2
%A A212823 _R. H. Hardin_, May 28 2012