%I #8 Jan 10 2019 15:22:16

%S 7,103,564,1980,5375,12327,25088,46704,81135,133375,209572,317148,

%T 464919,663215,924000,1260992,1689783,2227959,2895220,3713500,4707087,

%U 5902743,7329824,9020400,11009375,13334607,16037028,19160764,22753255,26865375

%N Number of length-5 0..n arrays with no following elements greater than or equal to the first repeated value.

%H R. H. Hardin, <a href="/A267234/b267234.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + (37/12)*n^4 + (5/2)*n^3 + (5/12)*n^2.

%F Conjectures from _Colin Barker_, Jan 10 2019: (Start)

%F G.f.: x*(7 + 61*x + 51*x^2 + x^3) / (1 - x)^6.

%F 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 (End)

%e Some solutions for n=6:

%e ..3....6....4....4....0....0....4....6....5....5....5....0....2....0....4....0

%e ..2....6....2....1....4....5....1....0....4....0....1....3....5....1....1....2

%e ..1....2....3....6....3....1....6....3....0....1....4....6....6....6....0....1

%e ..6....1....6....6....6....3....3....4....4....0....5....3....4....5....1....3

%e ..0....4....6....5....5....1....4....6....5....5....6....5....4....4....1....4

%Y Row 5 of A267232.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 12 2016