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A267231 Number of length-n 0..7 arrays with no following elements greater than or equal to the first repeated value.

%I A267231 #7 Feb 05 2018 17:09:55
%S A267231 8,64,476,3472,25088,180292,1291052,9222184,65755592,468196540,
%T A267231 3330042548,23664113536,168042120176,1192574364148,8459259667964,
%U A267231 59977781663128,425093823838040,3011867733313516,21333411555220100
%N A267231 Number of length-n 0..7 arrays with no following elements greater than or equal to the first repeated value.
%C A267231 Column 7 of A267232.
%H A267231 R. H. Hardin, <a href="/A267231/b267231.txt">Table of n, a(n) for n = 1..210</a>
%F A267231 Empirical: a(n) = 35*a(n-1) -518*a(n-2) +4214*a(n-3) -20489*a(n-4) +60515*a(n-5) -104992*a(n-6) +96516*a(n-7) -35280*a(n-8) for n>9.
%F A267231 Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F A267231 G.f.: 4*x*(2 - 54*x + 595*x^2 - 3437*x^3 + 11088*x^4 - 19495*x^5 + 16287*x^6 - 3546*x^7 - 1260*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)^2).
%F A267231 a(n) = (-7*(70 + 21*2^(1+n) + 35*3^n + 35*2^(1+n)*3^n + 35*4^n + 42*5^n - 627*7^n) + 60*7^n*n)/2940 for n>1.
%F A267231 (End)
%e A267231 Some solutions for n=6:
%e A267231 ..2....2....6....2....0....6....6....2....3....4....4....6....4....2....2....6
%e A267231 ..7....7....3....6....4....4....3....7....0....2....3....4....7....7....5....7
%e A267231 ..4....0....1....0....6....6....4....2....6....0....4....3....0....4....6....5
%e A267231 ..6....7....3....5....7....4....4....4....5....5....0....2....5....0....4....2
%e A267231 ..2....3....4....4....1....5....0....3....6....7....4....5....4....5....3....1
%e A267231 ..4....6....6....0....3....1....3....5....2....7....4....2....3....0....0....7
%Y A267231 Cf. A267232.
%K A267231 nonn
%O A267231 1,1
%A A267231 _R. H. Hardin_, Jan 12 2016