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%I #8 Nov 12 2018 14:41:57
%S 108,1989,14040,62041,206724,569693,1369136,2966769,5927452,11092917,
%T 19671048,33342153,54383668,85814733,131562080,196648673,287406540,
%U 411715237,579267384,801862713,1093732068,1471892797,1956536976
%N Number of length 3+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="/A250339/b250339.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (2/7)*n^7 + (28/5)*n^6 + (112/5)*n^5 + (109/3)*n^4 + (94/3)*n^3 + (166/15)*n^2 - (2/105)*n + 1.
%F Conjectures from _Colin Barker_, Nov 12 2018: (Start)
%F G.f.: x*(108 + 1125*x + 1152*x^2 - 635*x^3 - 308*x^4 - 9*x^5 + 8*x^6 - x^7) / (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=4:
%e ..3....2....0....2....2....0....0....1....4....3....4....4....3....2....0....3
%e ..1....3....3....0....1....4....3....4....2....2....0....1....2....1....2....3
%e ..3....0....2....2....0....0....3....0....0....4....3....2....4....1....1....0
%e ..3....4....2....3....1....3....3....1....2....3....1....2....3....0....1....3
%e ..4....2....1....0....1....3....3....1....0....0....3....3....3....1....0....3
%e ..3....2....3....2....4....3....1....1....2....3....3....2....3....1....4....3
%e ..0....0....0....2....0....3....3....4....2....3....4....0....2....3....0....3
%e ..1....2....4....2....4....4....3....1....2....4....3....0....3....3....4....0
%Y Row 3 of A250336.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 19 2014
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