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A267235 Number of length-6 0..n arrays with no following elements greater than or equal to the first repeated value.

%I A267235 #8 Jan 10 2019 15:22:24
%S A267235 8,223,1790,8274,27854,76237,180292,382404,745548,1359083,2345266,
%T A267235 3866486,6133218,9412697,14038312,20419720,29053680,40535607,55571846,
%U A267235 74992666,99765974,131011749,170017196,218252620,277388020,349310403
%N A267235 Number of length-6 0..n arrays with no following elements greater than or equal to the first repeated value.
%H A267235 R. H. Hardin, <a href="/A267235/b267235.txt">Table of n, a(n) for n = 1..210</a>
%F A267235 Empirical: a(n) = n^6 + (197/60)*n^5 + 3*n^4 + (3/4)*n^3 - (1/30)*n.
%F A267235 Conjectures from _Colin Barker_, Jan 10 2019: (Start)
%F A267235 G.f.: x*(8 + 167*x + 397*x^2 + 147*x^3 + x^4) / (1 - x)^7.
%F A267235 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A267235 (End)
%e A267235 Some solutions for n=6:
%e A267235 ..5....6....6....6....2....6....5....0....3....2....1....1....2....3....3....0
%e A267235 ..4....5....5....4....1....0....0....2....4....0....6....2....6....4....3....6
%e A267235 ..6....1....6....6....2....3....4....5....5....6....3....1....1....3....2....5
%e A267235 ..1....6....1....2....6....0....6....0....3....4....6....5....3....1....1....4
%e A267235 ..1....0....5....3....4....1....1....1....1....2....3....6....6....2....2....4
%e A267235 ..0....4....6....5....2....3....6....6....0....2....6....5....2....3....1....0
%Y A267235 Row 6 of A267232.
%K A267235 nonn
%O A267235 1,1
%A A267235 _R. H. Hardin_, Jan 12 2016