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A267466 Number of length-n 0..3 arrays with no following elements larger than the first repeated value.

%I A267466 #7 Feb 05 2018 09:35:33
%S A267466 4,16,58,204,712,2490,8770,31200,112300,409254,1510102,5638956,
%T A267466 21290368,81183858,312262954,1210023672,4718194516,18492663102,
%U A267466 72787129726,287468548548,1138446338344,4518338475786,17963524388818,71514144464784
%N A267466 Number of length-n 0..3 arrays with no following elements larger than the first repeated value.
%C A267466 Column 3 of A267471.
%H A267466 R. H. Hardin, <a href="/A267466/b267466.txt">Table of n, a(n) for n = 1..210</a>
%F A267466 Empirical: a(n) = 13*a(n-1) -65*a(n-2) +155*a(n-3) -174*a(n-4) +72*a(n-5).
%F A267466 Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F A267466 G.f.: 2*x*(2 - 18*x + 55*x^2 - 65*x^3 + 23*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)^2*(1 - 4*x)).
%F A267466 a(n) = (-18 - 9*2^(1+n) + 50*3^n + 9*4^n + 4*3^n*n) / 36.
%F A267466 (End)
%e A267466 Some solutions for n=7:
%e A267466 ..0....1....1....0....3....3....3....1....2....0....1....0....1....3....2....3
%e A267466 ..3....3....0....3....3....1....3....2....3....2....0....3....3....3....0....3
%e A267466 ..1....3....1....0....0....3....1....3....0....3....1....1....3....3....3....3
%e A267466 ..0....0....1....3....3....3....0....3....3....3....3....0....1....2....3....3
%e A267466 ..3....1....0....2....2....1....0....0....2....3....0....1....0....0....3....3
%e A267466 ..2....0....0....3....2....3....3....0....2....0....3....1....2....0....3....2
%e A267466 ..0....1....1....0....0....1....2....1....2....2....3....0....0....3....2....0
%Y A267466 Cf. A267471.
%K A267466 nonn
%O A267466 1,1
%A A267466 _R. H. Hardin_, Jan 15 2016