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%I A267234 #8 Jan 10 2019 15:22:16
%S A267234 7,103,564,1980,5375,12327,25088,46704,81135,133375,209572,317148,
%T A267234 464919,663215,924000,1260992,1689783,2227959,2895220,3713500,4707087,
%U A267234 5902743,7329824,9020400,11009375,13334607,16037028,19160764,22753255,26865375
%N A267234 Number of length-5 0..n arrays with no following elements greater than or equal to the first repeated value.
%H A267234 R. H. Hardin, <a href="/A267234/b267234.txt">Table of n, a(n) for n = 1..210</a>
%F A267234 Empirical: a(n) = n^5 + (37/12)*n^4 + (5/2)*n^3 + (5/12)*n^2.
%F A267234 Conjectures from _Colin Barker_, Jan 10 2019: (Start)
%F A267234 G.f.: x*(7 + 61*x + 51*x^2 + x^3) / (1 - x)^6.
%F A267234 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A267234 (End)
%e A267234 Some solutions for n=6:
%e A267234 ..3....6....4....4....0....0....4....6....5....5....5....0....2....0....4....0
%e A267234 ..2....6....2....1....4....5....1....0....4....0....1....3....5....1....1....2
%e A267234 ..1....2....3....6....3....1....6....3....0....1....4....6....6....6....0....1
%e A267234 ..6....1....6....6....6....3....3....4....4....0....5....3....4....5....1....3
%e A267234 ..0....4....6....5....5....1....4....6....5....5....6....5....4....4....1....4
%Y A267234 Row 5 of A267232.
%K A267234 nonn
%O A267234 1,1
%A A267234 _R. H. Hardin_, Jan 12 2016

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