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A267469 Number of length-n 0..6 arrays with no following elements larger than the first repeated value.

%I A267469 #7 Feb 05 2018 09:35:59
%S A267469 7,49,322,2072,13216,83972,532840,3381860,21491464,136856180,
%T A267469 873803848,5596638788,35973158152,232118471828,1503949949896,
%U A267469 9786663686756,63969334316680,420026972347316,2770499256109384,18356852895660164
%N A267469 Number of length-n 0..6 arrays with no following elements larger than the first repeated value.
%C A267469 Column 6 of A267471.
%H A267469 R. H. Hardin, <a href="/A267469/b267469.txt">Table of n, a(n) for n = 1..210</a>
%F A267469 Empirical: a(n) = 34*a(n-1) -490*a(n-2) +3892*a(n-3) -18529*a(n-4) +53746*a(n-5) -91860*a(n-6) +83448*a(n-7) -30240*a(n-8).
%F A267469 Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F A267469 G.f.: x*(7 - 189*x + 2086*x^2 - 12110*x^3 + 39543*x^4 - 71617*x^5 + 65212*x^6 - 22212*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)^2*(1 - 7*x)).
%F A267469 a(n) = (-504 - 315*2^n - 280*3^n - 315*4^n - 504*5^n + 3409*6^n + 360*7^n + 35*2^(1+n)*3^n*n) / 2520.
%F A267469 (End)
%e A267469 Some solutions for n=6:
%e A267469 ..3....1....4....3....6....2....5....4....5....1....4....3....6....4....3....2
%e A267469 ..6....5....2....5....0....6....2....2....3....6....5....0....2....6....0....4
%e A267469 ..3....2....5....6....5....0....5....0....6....6....6....3....4....1....4....1
%e A267469 ..5....5....4....4....6....6....1....6....6....3....0....5....4....0....6....5
%e A267469 ..2....3....5....2....0....6....3....6....3....0....2....4....2....6....1....5
%e A267469 ..5....0....0....3....3....6....6....5....0....5....1....0....1....1....2....1
%Y A267469 Cf. A267471.
%K A267469 nonn
%O A267469 1,1
%A A267469 _R. H. Hardin_, Jan 15 2016