%I #8 Nov 10 2018 12:43:59

%S 20,300,2040,8840,28860,77700,182000,383760,745380,1355420,2335080,

%T 3845400,6095180,9349620,13939680,20272160,28840500,40236300,55161560,

%U 74441640,99038940,130067300,168807120,216721200,275471300,346935420

%N Number of length 1+5 0..n arrays with no six consecutive terms having the maximum of any three terms equal to the minimum of the remaining three terms.

%H R. H. Hardin, <a href="/A250015/b250015.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + 3*n^5 + 5*n^4 + 5*n^3 + 4*n^2 + 2*n.

%F Conjectures from _Colin Barker_, Nov 10 2018: (Start)

%F G.f.: 20*x*(1 + 4*x + x^2)^2 / (1 - x)^7.

%F 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 (End)

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Row 1 of A250014.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 10 2014