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%I #8 Jul 21 2018 10:06:26
%S 1,2,5,13,43,152,559,2091,7882,29809,112895,427824,1621691,6147791,
%T 23307226,88363077,335007715,1270107208,4815336407,18256317315,
%U 69214939274,262413734345,994885963543,3771899000928,14300354743363
%N Number of 0..3 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..3 order.
%C Column 3 of A212829.
%H R. H. Hardin, <a href="/A212824/b212824.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) + a(n-2) - 6*a(n-3) - 3*a(n-4) for n>7.
%F Empirical g.f.: x*(1 + x + x^2)*(1 - 3*x - 2*x^2 + 2*x^3 + x^4) / ((1 - x - x^2)*(1 - 3*x - 3*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 ..0....1....1....1....1....1....1....1....1....0....1....1....1....0....1....1
%e ..1....2....0....1....0....1....2....2....1....1....1....2....2....1....1....2
%e ..2....3....2....2....2....2....0....0....2....2....0....3....2....2....0....2
%e ..2....0....0....2....2....2....3....2....2....3....2....2....2....3....1....3
%e ..0....2....3....3....3....0....2....1....0....1....3....1....0....3....1....1
%e ..1....2....2....3....1....0....2....0....2....2....3....3....3....2....1....0
%e ..1....0....1....2....0....0....1....3....3....0....2....1....0....0....2....0
%Y Cf. A212829.
%K nonn
%O 1,2
%A _R. H. Hardin_, May 28 2012
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