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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. 1

%I

%S 1,2,5,12,33,90,246,672,1836,5016,13704,37440,102288,279456,763488,

%T 2085888,5698752,15569280,42536064,116210688,317493504,867408384,

%U 2369803776,6474424320,17688456192,48325761024,132028434432,360708390912

%N 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 Column 2 of A212829.

%H R. H. Hardin, <a href="/A212823/b212823.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) for n>5.

%F Empirical g.f.: x*(1 - x - x^2)*(1 + x + x^2) / (1 - 2*x - 2*x^2). - _Colin Barker_, Jul 21 2018

%e Some solutions for n=8:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..1....1....1....1....1....1....0....1....1....1....0....1....1....1....1....1

%e ..2....2....1....2....2....2....0....0....2....1....1....1....0....0....2....2

%e ..1....0....0....2....2....0....1....2....0....1....2....2....2....0....0....0

%e ..0....0....2....2....0....1....2....1....0....2....2....0....1....1....2....2

%e ..0....1....0....0....1....1....2....0....0....0....0....0....0....2....2....2

%e ..1....0....0....2....0....0....1....0....1....0....0....1....2....2....0....2

%e ..1....0....1....2....0....2....2....0....1....0....2....0....1....0....1....0

%Y Cf. A212829.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 28 2012

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Last modified November 22 18:55 EST 2019. Contains 329410 sequences. (Running on oeis4.)