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Number of length-n 0..4 arrays with no following elements larger than the first repeated value.
1

%I #8 Feb 05 2018 09:35:43

%S 5,25,115,515,2285,10119,44901,200119,897301,4052183,18444197,

%T 84651063,391805877,1828676887,8604122053,40793238647,194778656213,

%U 936040595031,4524410973669,21981448319671,107275320299509,525571712299415

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

%C Column 4 of A267471.

%H R. H. Hardin, <a href="/A267467/b267467.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Conjectures from _Colin Barker_, Feb 05 2018: (Start)

%F 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 a(n) = (-80 - 15*2^(2+n) - 80*3^n + 335*4^n + 48*5^n) / 240 + 4^(-2+n)*n.

%F (End)

%e Some solutions for n=7:

%e ..1....3....1....4....1....2....4....4....3....1....2....1....1....3....4....3

%e ..4....4....4....1....3....1....4....0....3....0....3....4....2....1....1....1

%e ..4....3....0....3....1....3....0....3....1....2....1....2....3....0....3....4

%e ..1....4....1....3....3....0....0....1....2....4....3....1....1....4....3....3

%e ..4....2....3....1....4....1....2....4....1....2....4....2....0....4....0....1

%e ..1....1....2....2....4....2....2....2....2....3....1....0....4....4....0....0

%e ..0....2....4....2....3....0....3....0....0....0....3....1....2....3....1....4

%Y Cf. A267471.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 15 2016