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A267467 Number of length-n 0..4 arrays with no following elements larger than the first repeated value.

%I A267467 #8 Feb 05 2018 09:35:43
%S A267467 5,25,115,515,2285,10119,44901,200119,897301,4052183,18444197,
%T A267467 84651063,391805877,1828676887,8604122053,40793238647,194778656213,
%U A267467 936040595031,4524410973669,21981448319671,107275320299509,525571712299415
%N A267467 Number of length-n 0..4 arrays with no following elements larger than the first repeated value.
%C A267467 Column 4 of A267471.
%H A267467 R. H. Hardin, <a href="/A267467/b267467.txt">Table of n, a(n) for n = 1..210</a>
%F A267467 Empirical: a(n) = 19*a(n-1) -145*a(n-2) +565*a(n-3) -1174*a(n-4) +1216*a(n-5) -480*a(n-6).
%F A267467 Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F A267467 G.f.: x*(5 - 70*x + 365*x^2 - 870*x^3 + 920*x^4 - 326*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)^2*(1 - 5*x)).
%F A267467 a(n) = (-80 - 15*2^(2+n) - 80*3^n + 335*4^n + 48*5^n) / 240 + 4^(-2+n)*n.
%F A267467 (End)
%e A267467 Some solutions for n=7:
%e A267467 ..1....3....1....4....1....2....4....4....3....1....2....1....1....3....4....3
%e A267467 ..4....4....4....1....3....1....4....0....3....0....3....4....2....1....1....1
%e A267467 ..4....3....0....3....1....3....0....3....1....2....1....2....3....0....3....4
%e A267467 ..1....4....1....3....3....0....0....1....2....4....3....1....1....4....3....3
%e A267467 ..4....2....3....1....4....1....2....4....1....2....4....2....0....4....0....1
%e A267467 ..1....1....2....2....4....2....2....2....2....3....1....0....4....4....0....0
%e A267467 ..0....2....4....2....3....0....3....0....0....0....3....1....2....3....1....4
%Y A267467 Cf. A267471.
%K A267467 nonn
%O A267467 1,1
%A A267467 _R. H. Hardin_, Jan 15 2016