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A267465 Number of length-n 0..2 arrays with no following elements larger than the first repeated value.

%I A267465 #8 Feb 05 2018 09:35:22
%S A267465 3,9,24,62,160,418,1112,3018,8352,23522,67240,194554,568304,1672146,
%T A267465 4946808,14692970,43767616,130647490,390566216,1168815066,3500415888,
%U A267465 10488664754,31439779864,94264813642,282681194720,847808703138
%N A267465 Number of length-n 0..2 arrays with no following elements larger than the first repeated value.
%C A267465 Column 2 of A267471.
%H A267465 R. H. Hardin, <a href="/A267465/b267465.txt">Table of n, a(n) for n = 1..210</a>
%F A267465 Empirical: a(n) = 8*a(n-1) -23*a(n-2) +28*a(n-3) -12*a(n-4).
%F A267465 Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F A267465 G.f.: x*(3 - 15*x + 21*x^2 - 7*x^3) / ((1 - x)*(1 - 2*x)^2*(1 - 3*x)).
%F A267465 a(n) = 2^n + 3^(n-1) + 2^(n-2)*(n+1) - 1.
%F A267465 (End)
%e A267465 Some solutions for n=7:
%e A267465 ..2....1....2....1....2....2....1....1....1....0....1....0....0....1....1....2
%e A267465 ..1....0....1....0....1....2....2....0....1....1....2....1....1....2....2....2
%e A267465 ..0....2....0....1....0....2....0....1....0....0....2....1....2....2....1....1
%e A267465 ..1....2....1....0....1....0....1....2....1....1....1....0....1....2....0....1
%e A267465 ..2....2....2....2....1....1....0....2....1....0....0....0....0....1....1....2
%e A267465 ..2....0....1....0....0....0....2....1....1....1....0....0....1....2....2....2
%e A267465 ..1....2....2....1....0....1....0....1....1....0....1....0....1....0....2....2
%Y A267465 Cf. A267471.
%K A267465 nonn
%O A267465 1,1
%A A267465 _R. H. Hardin_, Jan 15 2016