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%I #8 Jan 11 2019 09:05:52
%S 1,2,5,13,34,88,225,569,1426,3548,8777,21613,53026,129712,316545,
%T 770993,1874914,4553588,11047625,26779909,64869586,157043368,
%U 380004897,919150313,2222499826,5372538572,12984354185,31374801373,75801065794
%N Number of n X 1 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
%H R. H. Hardin, <a href="/A267905/b267905.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) -7*a(n-2) +a(n-3) +2*a(n-4).
%F Conjectures from _Colin Barker_, Jan 11 2019: (Start)
%F G.f.: x*(1 - 3*x + 2*x^2 + x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x - x^2)).
%F a(n) = ((1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n) - 2*(2^n-1)) / 4.
%F (End)
%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....1....1....1....1....1....1....0
%e ..1....2....2....0....2....2....2....1....2....0....2....0....2....0....2....0
%e ..2....2....2....0....1....1....1....1....0....1....0....1....1....0....0....1
%e ..0....1....2....2....2....1....2....2....0....1....0....2....0....0....0....2
%e ..1....0....2....0....1....1....1....1....1....1....0....0....2....2....0....1
%e ..2....2....2....0....2....1....2....0....0....0....1....1....2....0....0....0
%e ..1....2....2....1....1....1....2....2....2....1....0....1....2....0....2....0
%Y Column 1 of A267911.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 22 2016
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