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%I #7 Aug 21 2017 06:22:26
%S 15,285,2010,8790,28785,77595,181860,383580,745155,1355145,2334750,
%T 3845010,6094725,9349095,13939080,20271480,28839735,40235445,55160610,
%U 74440590,99037785,130066035,168805740,216719700,275469675,346933665
%N Number of length 1+5 0..n arrays with no six consecutive terms having the maximum of any two terms equal to the minimum of the remaining four terms.
%C Row 1 of A249960.
%H R. H. Hardin, <a href="/A249961/b249961.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 + (3/2)*n^2 - (1/2)*n.
%F Conjectures from _Colin Barker_, Aug 21 2017: (Start)
%F G.f.: 15*x*(1 + x)^2*(1 + 10*x + x^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....0....3....4....2....2....3....4....3....1....0....4....4....1....0....0
%e ..3....4....1....2....4....5....1....2....3....3....1....2....1....6....0....3
%e ..3....5....3....5....3....5....3....0....6....5....0....4....6....4....3....4
%e ..5....3....1....3....0....6....2....3....6....2....2....1....5....1....6....1
%e ..0....2....3....5....4....5....3....1....0....5....4....1....1....3....1....6
%e ..4....0....2....1....4....3....3....6....1....0....3....2....2....5....3....4
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 09 2014
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