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%I #8 Nov 12 2018 14:42:21
%S 68,907,5264,20085,59396,147903,325312,651369,1211620,2123891,3545488,
%T 5681117,8791524,13202855,19316736,27621073,38701572,53253979,
%U 72097040,96186181,126627908,164694927,211841984,269722425,340205476,425394243
%N Number of length 2+5 0..n arrays with every six consecutive terms having the maximum of some three terms equal to the minimum of the remaining three terms.
%H R. H. Hardin, <a href="/A250338/b250338.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^6 + 9*n^5 + 20*n^4 + (68/3)*n^3 + 12*n^2 + (7/3)*n + 1.
%F Conjectures from _Colin Barker_, Nov 12 2018: (Start)
%F G.f.: x*(68 + 431*x + 343*x^2 - 96*x^3 - 20*x^4 - 7*x^5 + x^6) / (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 ..2....0....3....0....4....4....3....3....0....2....2....2....3....0....0....3
%e ..1....0....4....6....5....0....5....5....2....2....2....2....4....5....0....5
%e ..3....2....5....2....5....2....6....2....2....0....1....4....3....5....6....3
%e ..3....2....6....3....5....2....6....0....3....1....2....3....4....2....0....5
%e ..4....5....4....2....3....2....3....2....4....5....5....3....6....2....0....5
%e ..3....6....1....0....5....4....5....2....2....2....1....3....6....0....0....5
%e ..5....1....4....2....0....4....0....0....1....5....5....6....1....2....4....4
%Y Row 2 of A250336.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 19 2014
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