%I #8 Aug 21 2017 08:22:40
%S 15,505,5300,31180,129095,422065,1164800,2830080,6226935,12655665,
%T 24104740,43494620,74973535,124270265,199108960,309691040,469249215,
%U 694678665,1007250420,1433411980,2005680215,2763631585,3754994720
%N Number of length 2+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 2 of A249960.
%H R. H. Hardin, <a href="/A249962/b249962.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^7 + (13/6)*n^6 + (13/3)*n^5 + (65/12)*n^4 + (3/2)*n^3 - (1/12)*n^2 + (2/3)*n.
%F Conjectures from _Colin Barker_, Aug 21 2017: (Start)
%F G.f.: 5*x*(1 + x)*(3 + 74*x + 262*x^2 + 154*x^3 + 11*x^4) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F (End)
%e Some solutions for n=5:
%e ..1....5....2....1....3....0....5....2....3....2....3....3....1....3....1....2
%e ..4....1....1....2....4....2....0....3....0....2....0....0....5....0....1....0
%e ..5....5....0....4....0....3....5....0....5....2....5....3....4....1....2....0
%e ..3....5....3....1....4....5....1....1....5....0....4....1....5....3....3....4
%e ..0....3....4....3....5....0....0....2....1....0....0....4....5....3....3....4
%e ..2....5....2....5....0....5....3....0....5....5....2....3....2....3....2....3
%e ..0....5....2....1....2....5....1....4....2....3....5....3....3....0....1....3
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 09 2014