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%I #8 Nov 11 2018 09:18:28
%S 83,982,5604,21405,63611,159278,352192,708609,1323835,2329646,3902548,
%T 6272877,9734739,14656790,21493856,30799393,43238787,59603494,
%U 80826020,107995741,142375563,185419422,238790624,304381025,384331051,481050558
%N Number of length 2+5 0..n arrays with every six consecutive terms having the maximum of some two terms equal to the minimum of the remaining four terms.
%H R. H. Hardin, <a href="/A250083/b250083.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (7/6)*n^6 + (28/3)*n^5 + (245/12)*n^4 + (47/2)*n^3 + (227/12)*n^2 + (26/3)*n + 1.
%F Conjectures from _Colin Barker_, Nov 11 2018: (Start)
%F G.f.: x*(83 + 401*x + 473*x^2 - 106*x^3 - 5*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 ..4....4....1....2....4....0....4....4....2....1....4....3....1....4....4....0
%e ..0....2....6....4....0....5....6....6....1....2....6....4....5....0....0....3
%e ..0....1....2....6....2....2....4....5....3....5....1....1....5....0....3....5
%e ..0....0....4....6....2....3....0....3....2....2....1....3....2....6....3....2
%e ..3....3....2....1....2....2....5....1....5....5....1....1....4....0....5....2
%e ..6....1....5....2....5....3....4....3....2....5....4....1....2....2....5....2
%e ..3....3....0....2....3....0....4....6....4....0....2....4....2....4....3....1
%Y Row 2 of A250081.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 11 2014
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