%I
%S 15,4999,267004,5207128,55191061,389769865,2062131616,8794967112,
%T 31750272891,100377252987,284840809660,738995422048,1777772706385,
%U 4009552754989,8552986503328,17379265831600,33835476742695
%N Number of length 6+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 6 of A249960.
%H R. H. Hardin, <a href="/A249966/b249966.txt">Table of n, a(n) for n = 1..52</a>
%F Empirical: a(n) = n^11  (739/1260)*n^10 + (8033/1260)*n^9  (517/336)*n^8 + (191/210)*n^7 + (572/45)*n^6  (247/24)*n^5 + (653/336)*n^4 + (21293/2520)*n^3  (6337/1260)*n^2 + (37/35)*n.
%F Conjectures from _Colin Barker_, Aug 21 2017: (Start)
%F G.f.: x*(15 + 4819*x + 208006*x^2 + 2329714*x^3 + 9235434*x^4 + 14869326*x^5 + 10156734*x^6 + 2833778*x^7 + 273635*x^8 + 5339*x^9) / (1  x)^12.
%F a(n) = 12*a(n1)  66*a(n2) + 220*a(n3)  495*a(n4) + 792*a(n5)  924*a(n6) + 792*a(n7)  495*a(n8) + 220*a(n9)  66*a(n10) + 12*a(n11)  a(n12) for n>12.
%F (End)
%e Some solutions for n=2:
%e ..2....2....2....1....2....1....2....0....0....1....1....2....1....2....1....2
%e ..2....0....0....1....2....2....0....0....1....2....2....0....1....0....1....0
%e ..2....1....1....1....0....2....1....2....2....2....2....2....2....0....0....0
%e ..0....2....2....0....0....2....2....2....2....1....0....1....2....2....0....2
%e ..1....2....2....0....2....2....0....1....0....2....0....0....2....2....2....1
%e ..2....2....0....2....1....0....2....2....1....2....1....2....2....1....1....2
%e ..2....2....2....2....2....0....2....0....0....1....1....2....0....2....2....1
%e ..2....1....0....2....1....1....2....2....1....2....1....2....1....0....1....0
%e ..0....0....2....1....0....2....1....2....1....2....2....0....0....2....0....0
%e ..0....2....2....2....0....2....2....0....1....1....0....2....1....0....0....1
%e ..2....2....2....1....2....2....0....2....0....2....0....0....2....2....1....1
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 09 2014
