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%I #10 Feb 06 2018 04:16:32
%S 3,9,21,47,103,223,479,1023,2175,4607,9727,20479,43007,90111,188415,
%T 393215,819199,1703935,3538943,7340031,15204351,31457279,65011711,
%U 134217727,276824063,570425343,1174405119,2415919103,4966055935
%N Number of length-n 0..2 arrays with no following elements greater than or equal to the first repeated value.
%C Column 2 of A267232.
%H R. H. Hardin, <a href="/A267226/b267226.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) for n>4.
%F Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F G.f.: x*(3 - 6*x + 2*x^3) / ((1 - x)*(1 - 2*x)^2).
%F a(n) = 2^(n+1) + 2^(n-2)*n - 1 for n>1.
%F (End)
%e Some solutions for n=6:
%e 1 0 0 1 2 0 1 2 1 1 0 2 1 1 2 2
%e 0 2 1 2 0 2 2 1 0 2 2 1 2 0 0 1
%e 2 2 2 0 1 0 1 2 1 1 0 0 0 2 2 0
%e 0 0 0 2 2 1 2 0 0 2 1 1 2 2 2 1
%e 2 0 2 1 1 1 0 2 1 1 0 1 0 1 1 2
%e 1 1 1 1 0 0 1 1 1 1 2 0 1 1 0 0
%Y Cf. A267232.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 12 2016
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